There has been considerable change in these mores over the years - just like Delhi has seen influx of Punjabi Sikhs post-Partition (Sikhs who were driven out of Pakistan) - similarly the muslim residents of Delhi who emigrated or were driven out from India have taken on many Punjabi or local traits - and dropped some of the more local behaviors.
Among cultured muslims (of old Delhi for instance) the usual way of saying "Salaam" or greetings would be by saying "Adaab" (i.e. short for "Adaab baja laitay hain" where "Adab" means respect (or actually Adaab usually means "culture") - so something like "we are arriving and bringing with us respect for you or something like that"). - although very religious types in Delhi may still have said the full "Assalam-u-Alaikum" (i.e. peace and blessings be on you). But generally "Adaab" was preferred in the "cultured" classes - while "Assalam-u-Alaikum" was seen as more pedestrian (shocking as it may be) - and the reason for this is probably that in the mileu that appeared in the Mughal environment - there was a conscious effort to make the ways of life (or at least the areas where they interacted) more neutral between Hindus and Muslims. After all it would have been greatly disconcerting if Hindus and Muslims had very different behaviors in court for instance - one touching feet while other shaking hands or hugging or just saying salaam from afar - in any case probably security would have dictated that hugging not be done in the royal court - and otherwise the muslims may have learnt something from the Hindus - and avoided shaking of hands. Since "Adaab" effectively does away with the need to shake hands. Also a plague or two may have convinced some muslims that the Hindu way was better i.e. salaam from afar.
You will still find some families where people will say "Adaab" - but will usually be families where both sides of the family are from Delhi, Lucknow etc. If one of the parent is from Punjab or other - then you are likely to see significant decline in this element. And the reason is that saying "Adaab" is considered "funny" by many Punjabis for some reason - I have heard punjabi women giggle on hearing it - perhaps it is because they associate it with or have only heard it in movies like Umrao Jan or something or they find it "quaint" or whatever. Or perhaps it was originally a "hindustani" thing - since after all it is not pure islamic but an outcome of a mix of cultures (as outlined above).
This is similar to the change that has happened in Delhi - where the local old Mughal environment is now perhaps dominated by migrants who had to leave Pakistan (usually Punjabi Sikhs) - so now the "culture" of Delhi is perhaps dominated by new inhabitants - and only occasionally will you see the "old families" i.e. muslim or hindu who still have the old behaviors.
Similarly in Pakistan - there has been a HUGE mish-mash of cultures and people - with muslims coming from Delhi and Lucknow and south india etc. etc. - all mixing and living together or in near proximity to each other - for example in places like Karachi. And in near proximity to local inhabitants of the place - like in Lahore. This has led to considerable mix in language traits - so in Karachi those "urdu speaking" families who had to live in slums acquired some of the influences from there. More recently even children of "urdu speaking" families have started speaking "Q" as "K" in Karachi (a very Punjabi trait).
In Lahore oddly enough among the old working class inhabitants - a "K" is sometimes pronounced "Q" by the local classes - and a "Q" as "K" - this probably stemmed from confusion (even from pre-Partition days) - of a local Punjabi environment which tried to emulate the language of the upper crust speaking Urdu - at least that is my guess (otherwise why the compulsion to even try to speak "Q" ?). But this is something that predates Partition. This problem is similar to the problem "R" and "L" that is stereotypically attributed to Chinese speakers (as in "I want to eat some Lice") - and is a common confusion in languages which are missing a sound (and so they cannot distinguish between the two sound "hey, it sounds the same to us").
Regarding holding hands to chest - that is something that is often done by some people after shaking hands - usually perhaps to signify that "something close to the heart". Or to suggest that "Alhamdollilah" i.e. all praise to god things are ok here type of thing in response to someone asking you are you ok. However, this is something that you will see at all levels of society - i.e. even those from rural areas will do this. So it may have religious roots. But it is not something two "yaar" will do - so is suggestive of some type of politeness and formality.
Regarding the bending slightly while embracing - that is "natural" in that if you are meeting someone much older than you (who you do not want to dominate over - for example if you are tall - you don't want them seeming like they are your kid etc.) - then you will stoop while embracing - this is only natural as one feels awkward if an elderly person (who is short) is in your "baghal" i.e. armpit while embracing.
In the context of meeting "your nani" or let's say some elderly lady from your family (or even an older male "Nana" type figure) - at least among "urdu speaking" types i.e. the ones who migrated from Delhi, Lucknow etc. - there IS a tendency to bend your head down - and this is because you anticipate that they will stroke your head.
So the bending of the head while meeting an older lady - would be in anticipation that your head will be stroked affectionately by the lady. It is also the custom in many older families (and may be also in Punjab and rural areas) - that a younger person will "seek ashirwaad" (as would be said in India) - and here you are essentially prepping yourself to be touched on the head. It is not very common generally - but among close family and or affectionate older lady (who has perhaps seen you in diapers) - you would anticipate that she is holding up her hand and suggestive of wanting to stroke your head - so this would then trigger the bending reflex - which would be slightly awkward in modern times but you would do it given the signals being given. Anyway so that is a modern interpretation of it :-) Obviously earlier it would be much more natural as people would be doing this all the time. But this probably varies by family.
Often you will even find let's say a politician who is affectionate meeting an old lady in a village (his constituent) - and she may pad him on the head - and he will bend his head.
Although now I have seen Shehbaz Sharif patting the head of older lady also - like a flood affectee etc. - and it is mildly offensive I feel - but perhaps he is acting like he is protector now - in any case people may differ on this .. but anyway ..
Regarding touching of feet - usually this is extremely uncomfortable for a muslim when someone does this to him - and is similar to how some hindus also behave when they don't want to subject the other part to that - for example if someone does that to Amitabh Bachhan on KBC - he will shy way and say "please please" - that type of thing. But also since muslims are not exposed to that generally that is also reason for feeling odd - but also the comment about "not bowing before anybody but God" is there as well - i.e. "TECHNICALLY" you should not bow before anyone (even your King) - so if there is some bowing as a mark of deference - usually you will find it will be minimal. Although historically I am sure there have been times when people have bowed before the king - and I am sure in rural contexts when a Haari is begging his landlord to forgive him or something he will be touching the feed of the cruel landlord etc. etc. - so I am sure some of these traits do exists in society - as extreme mark of desperation.
However on the subject of feet - it IS an established understanding that "paradise lies at the bottom of the mother's feet" (in islam) - so in that sense it would not be uncommon for some trait of touching feet of mother figures to happen in some instances I suppose. Anyway it will happen if children are "dabaoing" i.e. pressing feet of elder etc. so it is not like touching feet is taboo in that sense.