I'm a research assistant!
Hmmm...So, we don't buy cakes all the time for birthdays. If someone feels so inclined, they'll bring one in. Otherwise, the birthday passes by quietly. I agree it seems weird that you are asked to get birthday cakes!
Also, my PI has an administrative assistant (...secretary...) who would make fliers for him. But I'd be surprised if they were ever non-lab things.
My team has been talking about making a website, but I'm actually pretty excited to do it. I've just been so swamped lately that I have no idea when I'll have time to do it.
Research assistants have jobs! I am probably the hardest worker my age in our lab...the other assistants are really technicians (I distinguish between the two because techs do the same protocols every day, typically preparing samples for experiments by researchers, while I help develop technology, have input in my experiments, do literature searches, have different experiments to run all the time, read over grant requests...all sorts of miscellany). They tend to have a lot of spare time. They take long lunches and hang out with each other randomly during the day. They still aren't asked to do personal things like you are, though.