Can I use Wifi for internet, and LAN on internal network only

You should not connect the same computer to both wired and wireless at the same time.  If that is what you are doing, it will cause issues with speed.

you have several options, mainly if you have two routers, one from your internet provider and another one you are using for wifi - you can disable internet access on the second one You can connect to and configure each. But overall, I am a little confused about what your goal is

You can use a WiFi to Ethernet bridge. 

https://amzn.to/3WU4KaV

Takes Wifi as input, Ethernet to your PC as output.

Hi I am currently using wifi for my internet and am quite happy with it, but unfortunately my wifi does not work with Wake On LAN.

WOL only works on my LAN card. my computer is not in a position to connect to LAN by cable, so I have it connected to my router using a wireless powerline transmitter.

While this is connected my internet speeds are very poor even though I am connected to both the LAN and Wifi networks at the same time. If I disable lan, the speed improves again, but I cannot use Wake On LAN.

Is there a way I can use my LAN only for thr internal network and use my Wifi for internet?

I got this,...

You want something like this

To be really clear, I am not recommending this particular item. In fact this item is probably total crap since it was on the top of Amazon's sponsored list.

I used to use one of these to connect my DVD player to my network since it only had ethernet. In your case, you would plug it into your computer - make sure you get one that is compatible with WOL. Try Microcenter to find something not made by random slave labor. Anything like this from Amazon marketplace is probably either a forgery or junk unless it comes from the manufacturers store.

IMO, you should never (ever) use your personal computer over WiFi unless you really have a good understanding of internet security. I suggest you get your ISP to move your router next to your computer, and then set up a subnet if needed.

I have a WiFi receiver downstairs than connects to a switch to provide ethernet to things like my server, 3d printer etc. It is really easy to set up, just watch some YouTube videos.