There’s a thing called Birth Order theory and it may or may not be bullshit and subject to cognitive bias, but I will say that anecdotally it seems mostly accurate when I think of my group of friends growing up and their siblings. There are definitely some exceptions though, like my friend who is the younger brother, but is more responsible than his big bro, though we suspect the older brother suffers from some sort of undiagnosed mental illness and is unwilling to get checked out. Short answer in my opinion is yes, the older sibling tends to mature faster. I do think that the older sibling has some power over the younger ones by virtue of being older and more mentally developed while growing up. Whether they use that to nurture and protect, or abuse the younger sibling is more a matter of personality than birth order though.

For your second question about feeling immature, I think it can happen to anyone at any time. Being put in a tough situation and feeling helpless about it can make a grown person feel like a child, despite being an otherwise mature adult. For me it happened less the more I became independent. But it still happens. For example, if car issues pop up I can get the feeling of “oh shit, I need an adult”. I think personality is a big factor here too. As an only child my perception is that I feel less willing to ask for help than others, at least until I try to find a solution myself. Some friends who were younger siblings seemed to always be getting catered to, getting rides to places, etc. That might also be influenced by other factors like family’s finances.