This is kind of a contradiction in itself, if you have a wired backhaul, you just need a dumb AP - meshing (and there are multiple, mutually exclusive and incompatible implementations for this) only matters if you're looking for a wireless backhaul. For these wireless uses a dedicated backhaul (third-) radio does offer significant advantages (Linksys EA8300/ MR8300 comes to mind), if you have a wired backhaul you have many more (cheaper) options.
This might be a bit more difficult on ipq40xx based devices than on other SOCs, not impossible (especially looking longer term, with the upcoming move to the DSA switch driver framework, but you will have to check your needs if you need those features now).
Not realistically possible. Yes, you can configure LACP, but most of your devices are still restricted to a single 1 GBit/s CPU port, which -especially for AP uses- limits your aggregate throughput to that maximum (and with 4+1 ethernet ports tops, LACP doesn't really provide any benefit for hardwired/ switched traffic either).
Good luck…
Here you leave your price bracket.
If I'd live in north america, I'd look into the https://openwrt.org/inbox/toh/askey/askey_rt4230w_rev6, yes availability doesn't quite tick the "new" checkbox, but they're still plenty on the used market and cheap (~40 USD). Very capable hardware (ipq8065+QCA9984), no VLAN weirdness, downsides involve that support for them hasn't been officially merged into OpenWrt yet and the initial installation being a tad more difficult; no, PoE and high ambient temperatures won't be met by this device either, but you can get ~ten of those very capable high-end devices within your budget.