Holding the door open I feel is one of those 'old' style things put on men to be polite to women, or the elderly because of gender roles and sexism, women 'the weaker sex'. If I hold a door open, meaning I wait for them to get in/out, I do it because the person is a child/elderly person/otherwise has mobility issues/burdened with items. It is less often that anyone, especially a women will hold a door open for me except in the situation that I am burdened with items. I also find men are more likely to at least hold the door open if they are in front of me so I don't have to open it myself, but they don't wait for me to fully enter/exit, something I also do for those behind me.
Opening the car door for a women I see as 'fine' especially if it is locked and you use a key, closing it to me seems more like she isn't capable of doing it herself, sort of like tucking her in, but that's my view. I tend to think that is 'too much' unless it is a really formal setting like being out with in-laws, a business trip, or perhaps a first date but the date would probably need to be 'fancy'.
I don't know what one would call an older women, if it were obvious she was older, besides ma'am. I used miss at one time but didn't know that was 'supposed' to be for younger women. Honestly if there is another term to call an older women you don't know I'm drawing a blank. Beyond that I sometimes avoided using ma'am or miss and went with no identifier, ie excuse me or directly to asking a question or whatever my purpose was about.
In a formal setting, I can see standing when a women enters a room, but beyond that it seems really dated.
As a rule unless someone has literally a handful of items like 5 or so and I have a ton I don't offer anyone the option to skip me. It is extremely rare I have a 'lot' of stuff that someone waiting for me is going to be held up enough to warrant me letting them skip me. I also don't take my cart load of crap into the express lane or the shortest lane that other people with one item will line up behind me. This has happened on the automated scanners built for people to take a cart load of groceries, there are 4 scanners for express self scan and 2 for cart load self scan many people overlook the cart self scan and sometimes lineup behind my cart with their two items I do not offer them to jump me as they always come after I've started scanning.
That's my perspective, in my early 30's, and people have all sorts of views on these things. I'm sure as I see some of those things as dated there are some people that would think me rude for not always doing them.