Just set old router to AP Client mode if supported, and You’re good to go.

Given it has decent ping and upload, I think You will be fine.

Connect shop router via LAN port instead of WAN. If with that bridge mode it refuses to work afterwards, check if You can set is as regular Access Point, set IP address manually and it should work, as You speak above, bridge mode seems familiar, but You don’t write up it’s addresation, did You set this up, or You need to maintain it from the app or something like that? Usually principle is, that if You want router to stays in the same network and act as AP, with no translation by the way, You plug it with LAN port. Maybe it’s just that, check it :)

It depends really. I’ve install new WiFi bridge in 2016, and change UTP that goes by the wall in like 2020, as it change color and start to cracks. But other cable, which were installed in 2003 is fine, little bit stiffer than new one, but no cracks and still working well, same side of the house, may have little more shadow, but 20 years and it is regular cat5e cable, not outdoor one :P guess materials were better back in the days.

I agree with just painting those cables. Or to put those in cable conducts, not prettiest solution, but cables hanging loose is neither.

Best for You is to firstly set providers router, which You probably has/get to bridge mode (so it will not acs as a router) if You can, and leave routing by You routers side. Or maybe You just get media converter from fiber to RJ45, that’s even better. In this scenario, You put router in some good spot (probably just center of the house, maybe near staircase, rather higher than lower, imagine signal boucing off the walls and going thru doors) and You’ll need to run two UTP cables to router - one from your ISP hardware to the WAN port, second to run back to place, where all of Your wiring meets, from LAN port of the router. There You have to place network switch, they usually comes with 4, 8, 16 ports, etc, so if You have 8 endpoints, then You will have 9 cables (1 from router, 8 from rooms) so best is to buy 16 port switch. If You can’t put ISP device in bridge mode for some reason, then it is pointless to have 2 routers on network, so You sets Your router of choise to Access Point mode, and in this case You need to provide it with just one cables and put it in the LAN port, as it don’t need to translate ISP network to local one. At this point, You can consider to put small rack case, end cables at patchpanel, buy rack switch, connect them with patchcords and make it pretty ;) but You can also just terminate them with RJ45 plugs, plug it to regular switch and it will work the same. 1 Gigabit is standard for now, but You can consider going for 2,5Gb devices, tho it isn’t necessary as You can always upgrade even to 10Gb, even if You have cat5e wiring (but if I can choose, then I’ll go with 6e). It also depends if Your ISP have 2,5Gb port in device that they provide to You, and what kind of speed they offer. And 1Gb devices is cheaper, as 2,5 is relatively new thing. If You have big house, it is always batter to go with multiple APs, than to buy overpriced premium router, which just can’t cover all off that. That being said, i have like 300 meters square brick house (Europe here :P) and single AX TP-Link cover it all just fine - i just place it at good spot. Tho all PCs is connected by wire.