Hi there :D

1: what game engine would I use?

 Well, you should decide what kind of game you are going to create. Is it 3D or 2D? choose proper engine which could be used to create your choice.

2: I have a Intel desktop but it's an i5 with a integrated graphic chip, no actual graphics card. Can I still make a game with that?

I'm not familiar with specs like this but there should be engines for low spec PCs.

3: if I'm new to coding and I don't plan on having a game done for at least 2 more years,  what language would I even learn first?

This should be fitted to your chosen engine.

4: I'm not the best at art or drawing but I'm always practicing to improve. What applications could I use for making my own assets? I know they are gonna look a little crusty. But if I can practice now it will help later!

Again, as mentioned in #1, you need to decide if your game is going to be 3D or 2D. From the answer you can choose proper apps to create your assets.

5: how do you stay motivated?....

1. Create game that you really love. Don't make game because it's popular, famous or current trend! Make a game that you really love even if only a few people play this kind of game.

2. Have enough break and sleep.

3. Play some games preferrable ones with same genre as the one you're making.

Good luck with your game :D.

I made an entire list of every game engine and their flaws: https://itch.io/blog/865134/every-game-engine-explained-and-why-they-all-suck

The engine is up to you, me personally because I cant learn how to code normally I use Construct 3 but also Gdevelop is about the same and 100% free.

Of course! I started out using my schools $20 cromebook lmao

That will be decided mainly by the engine you choose, although I have heard Lua is very easy.

https://www.piskelapp.com This is what I started out and still use, I also use Aseprite but Piskel works just the same for free with less features

Whenever one of my projects is failing I always think of what I learned from the project and not how it came out, even your worst most unplayable games are a learning experience.

Also one other tip that I can give is try to create easy systems for adding new things, like for instance if you have a bunch of weapon ideas don't add them all at once. Add one and then write the code in a way that you can either reuse it or copy and paste it for the other weapons instead of manually adding them all