TP-Link Litewave 5 Port Gigabit Ethernet Switch | Desktop Ethernet Splitter | Unshielded Network Switch | Plug & Play | Fanless Quiet | Unmanaged (LS1005G)

As long as everything is on one subnet/VLAN, it doesn't matter if the clients are wired or wireless. Turn on the one DHCP server you want to use, and disable all others. If you have more than one DHCP server running on the same LAN, you'll get weird results. Clients broadcast a request for DHCP, and the DHCP server sends a response to that. If you have multiple DHCP servers, your client will get different responses depending on which server happens to respond to the request first. And remember that it's Dynamic Host Configuration Protocol. DHCP just sets your network configuration for you so you don't have to do it manually. Whereas something like a DNS server provides an ongoing service to clients (converting domain names to IP addresses), DHCP just configures your network settings when you connect, then isn't used again. If you have a lot of clients and/or clients that frequently switch to other networks (like your phone that you take all over with you), DHCP saves a ton of manual work. But if you just have a few devices that stay connected to the same LAN, it's not that much effort to manually set their DNS server once. Your "switch" sounds more like a whole "broadband router" if it includes an AP and DHCP server. If you're not using its extra features, it might be simplest to just replace it with something modern and standard. I'm inferring that you wouldn't mind having more Ethernet ports - you can get an 8-port switch for $20. https://www.amazon.com/dp/B00A121WN6/ If a 5-port will do, it's only $10. https://www.amazon.com/dp/B0863M7C1L/

You only want one router on your network, and it has to be right after the modem. Adding another router creates a second LAN, which will isolate your client devices that are behind it, and could even conflict with the first router/LAN if you don't have it configured correctly. If you disable all the routing functionality of the BEFSR41, you could use it as a 100Mb network switch. However, the fact that you also had problems with it on a different connection suggests it might be at least partially broken. Just spend $10 and buy a small gigabit switch. https://www.amazon.com/dp/B0863M7C1L It will Just Work™ when you plug it in, and it'll be 10x as fast.