I've been there. I ended up buying an ASUS-RTAX53U, flashed it with OpenWRT, since it supports VLANs. You have full control over your device. For switches I'm using zyxel 8 port managed ones. Having 4 ssids, Im satisfied, and can be done pretty cheap. If you want to get started check OneMarcFifty's tutorials.

Can be a lot of things. For my parents problem was the old lan card in pc, which was 10/100. Can be router port, switch port, cable. How do you measure it? Can you plug ur pc directly to the modem or router?

Mesh or wireless bridge?