All LVP is actually waterproof. It's a very solid option for basement flooring because of this. That being said though, remember that you should never leave water sitting on your flooring, whatever that flooring, for weeks on end. The water won't damage you LVP, but it will eventually seep through to the bottom floor and gradually cause damage and become a huge insurance problem. You can measure against this though with the installation of a moisture trap depending on your situation. Another thing about LVP, is the option of ER or Embossed in Register. With ER, the texture of the plank matches up perfectly with the register or the original graphic. This means that every grain is captured in detail, including wood knots. An advantage of this is increased surface area so it protects against slipperiness and you from falling. Here's the main link I used to learn about ER and LVP if you'd like more information. I hope this helps!: https://www.reallycheapfloors.com/blog/the-best-flooring-for-basements/

Currently the floor can receive sheet goods - that's it. Carpet, sheet lino or sheet vinyl. The wonkiness of the concrete prevents everything else. To correct the wonkiness, you need to have the paint removed = abatement. Which is something you don't want to do. Mind you, once the abatement has occurred, you can go ahead and have the concrete flattened/dealt with and then you can have ANY FLOOR you want. Whenever you want. For as long as you want. Until then, you can work with "sheet" materials like carpet, lino or vinyl.

What ever you want. Your location will dictate your choice of materials. Some like carpet. Others will choose laminate (low cost = don't have the budget). Some want hardwood. Others choose tile (not my choice). And some will even go with cork. Your aesthetic will also help dictate your choice of materials. If you actively chose concrete because it was the aesthetic you were after (not for financial reasons...leaving concrete bare) then you will need to let us know a little bit more about where you live and your design preference.

I have always liked the slate or slate look flooring with wood paneling. Maria Killam has a post where she shows some great matches of LVT to wood floors - we've come a long way in the look of LVP, so I wouldn't just say it all looks fake next to the real thing. I don't think I would want wood look LVP with your wood paneling, but it could be done if that is what you like. I agree with palimpsest that you could find some nice tile or stone look LVT. I think this might be nice with your walls or possibly this: