I don't know if this is a little off topic, but I'd like to interject with respect to Arjuna and Draupadi's relationship. I read here that Arjuna apparently didn't care for her. I don't claim to be an expert in the epic and have read only the Adi Parva linearly while I read the other Parvas in part, until now, my impression has been that he does care about her, very much. I don't have citations to back every one of my claims but I'll still write what I know first-hand and secondhand.
In the beginning, when they met, he along with Bhima stands up to defend her despite not having to, since the kings are ready to let Arjuna go. They only want to get to Draupadi. Here is the citation where they explicitly state that-
"O kings! If this lady does not wish one of us as her husband, let us throw her into the fire and return to our kingdoms. Though that Brahmana has done injury to kings out of his impertinence and greed, he should not still be killed. After all, our kingdoms, lives, riches, sons, grandsons and all our other wealth exist for the sake of Brahmanas."
Next is the controversial statement about Arjuna suggesting polygamy. Which makes little sense. Here's the citation-
Arjuna said, “O king of men! Since this is not the law that others accept, do not make me tread this path of adharma. You should marry her first, followed by the mighty-armed Bhima of wonderful deeds, then I, then Nakula after me and finally the energetic Sahadeva. O king! Vrikodara, I and the twins think that the lady should be yours. This is the state of affairs. After reflecting on it, please do what is appropriate, in accordance with dharma and fame and the welfare of the king of Panchala. Instruct us. We are all waiting for your command.”
KMG apparently translates this better. But here it seems that it is Arjuna who first proposed Polyandry. But that makes no sense since the very next sentence he contradicts it himself. And then asks Yudi to make a decision. If he already thinks Polyandry should be done, why deflect it to Yudi again? And then, there's the specific mention of Drupada, who we know was none too pleased with the Polyandry. Besides nobody reacts to Arjuna's possible suggestion of Polyandry. And later we get into Yudi's head-
"Panchali’s charming form was created by the creator himself. It beguiled all living beings and was supreme to all others. Kunti’s son Yudhishthira knew from their appearance what was going through their minds. O bull among men! He remembered Dvaipayana’s words. Fearing that conflict might arise between the brothers, the king said, “This fortunate Droupadi will be a wife to all of us.”’
To me, this reads like a decision Yudi took by himself. He remembers Vyasa's words and fears conflict but if his younger brother had already suggested this solution why doesn't Yudi think of those words? Why are Vyasa's old words mentioned but Arjuna's latest suggestion isn't? It clearly seems to me like a decision Yudi took based on a few facts, like the evident attraction every Pandava had for Draupadi and the fact that it could be a cause for conflict. Also, Kunti plays no part in this except later where it seems she's supportive of the decision. Further, all the Pandavas actually think about this decision.
Vaishampayana said, ‘Hearing the words of their eldest brother, all of Pandu’s sons, of infinite energy, were pleased and began to think about the purport of those words.
If Arjuna had already suggested it, this would have come much earlier. For me the sequence of events is that Arjuna actually suggested that Yudi alone should marry her, something that seems to be the collective decision of all four Pandavas but fearing conflict, Yudi decides on Polyandry instead.
As for Arjuna having weapons in Draupadi's room, that's not true. It's Yudi who was 'lying' with Draupadi in the armory, because reasons. Here's the citation-
‘On hearing the words, the mighty-armed one told the brahmana not to fear. But Dharmaraja Yudhishthira was then lying with Krishna in the room where the great-souled Pandavas kept their weapons."
Moving further into the Dyut Sabha, the one statement of Arjuna was very much important according to me. But it didn't free the Pandavas. Duryodhana only offered to free Draupadi. This is Duryodhana's offer-
Dhritarashtra’s son smiled and spoke these words to the daughter of the king of Panchala, “O Yajnaseni! Let the question now be placed before the immensely powerful Bhima, Arjuna, Sahadeva and your husband Nakula. Let them reply to your words. O Panchali! Let them declare before all these aryas that Yudhishthira is not your lord. They must establish Dharmaraja as a liar.You will then be freed from servitude."
He is offering to free her from servitude on the condition that one of the Pandavas declares that Yudhishtira is not her lord. Things happen in between but I will come straight to Arjuna's reply.
Arjuna said, “This great-souled King Dharmaraja, Kunti’s son, was certainly our master when he first played with us as stake. But whose lord was he, once he had lost himself? O assembled Kurus! All of you should decide that.”’
Duryodhana's condition is that one of the Pandavas should say that Yudi was not Panchali's Lord. Arjuna fullfills this. And Panchali is by Duryodhana's own words, free. Immediately after this some omens occur, and Dhritrashtra who didn't move a muscle until now, is actually nudged into action. If we look at this rationally it's clear that Arjuna's words at least in part, spurred Dhritrashtra. Not only that, they actually shut Duryodhana up. He couldn't prevent Draupadi from doing anything now since by his own words and Arjuna's Draupadi was no longer in his control. She could do what she wanted. If this isn't the case what stopped Duryodhana from arguing with Vidura again? His whole plan was being undone and he just kept quiet for no reason? I find that hard to believe. For me, the reason is that he was trapped with his own words.
Another thing I would like to point out in this scenario is the similarity in Arjuna and Draupadi's thought process. Here's the citation of Draupadi's words regarding Yudhishtira in Dyut Sabha-
Droupadi replied, “Though he is himself unskilled, the king was challenged in this sabha by those who are skilled, evil-minded and deceitful, those who love the game of dice. How can it be said he chose voluntarily? The pure-hearted and foremost one among the Kurus and the Pandavas was robbed of his senses by inclinations towards deceit. He has understood everything only after he has been won and after the gambling is over. In this assembly hall are Kurus who are the lords of their sons and daughters-in-law. Let all of them examine my words and answer my question in the appropriate way.”
Here are Arjuna's words to Bheem when the latter wants to burn his hands-
"The king was challenged and he followed the dharma of the kshatriyas. He gambled because of the desires of the enemy."
Both say the same thing. He was challenged and decieved. But later in Vana Parva and many other times Draupadi makes it clear that she (rightfully) blames Yudhishtira. And on 17th day Arjuna too makes his feelings known. So it seems both privately blame Yudhishtira but publicly defended him.
Further in Vana Parva, according to KMG, after Krishna announced that all her enemies will be killed, Draupadi looks to Arjuna for reassurance. When he leaves, she speaks a whole paragraph about how much she misses him, in the presence of her other husbands, but this isn't about her. When Arjuna returns from Indra-loka, he brings jewelry for her. When he hands it to her she is explicitly stated as his 'love', Sutasoma's mother. Further down the line in Virat Yudh, a very interesting conversation takes place between Arjuna and Karna where the former specifically mentions Panchali.
“O Karna! You uttered many proud words in the midst of the assembly hall, to the effect that there was no one who was your equal in war. Disregarding all of dharma, you spoke harsh words. But I think that your wish is impossible to accomplish. You ignored me and spoke words earlier. O Radheya! Now, with me and in the midst of these Kurus, make that true. You watched when evil-souled ones oppressed Panchali in the assembly hall. You will now reap the fruits of that. Being bound down by the noose of dharma, my rage was restrained earlier. O Radheya! You will now witness the victory of my anger in battle. O Karna! Now fight with me and let all the Kurus and their soldiers witness it.”
Later too, Krishna mentions to Sanjaya that Karna's words in the assembly hall, were buried in Arjuna's heart and hurt him. (I can't quote verbatim here). There is no one who knows Arjuna's heart as well as Krishna.
On 17th day of battle when Yudi and Arjuna argue, the latter mentions Draupadi again, airing his resentment regarding the sharing that happened years ago. He says something like- "Sitting in Draupadi's bed, you insult me."
We learn from Sanjaya that when Krishna, Arjuna, Draupadi and Satyabhama are sitting together, no one is allowed to interrupt them. This clearly speaks of a close friendship between the duo of Arjuna and Draupadi.
These are some things that I know, as of yet. To me it seems like Arjuna did care about Draupadi though like most other stuff he wasn't exactly very verbal or expressive. But more importantly, not only were they spouses, but close friends too. She had a close, unique bond with her third and allegedly dearest husband, which is subtly shown in the epic.