Hey.

Well, my vocal range is that of a bass (E2-E4), but I really want to hit those high notes. I don't want to sing like fucking Rob Halford but I feel really limited when I'm singing, because I feel like I can't emphasize my vocal lines and that frustrates me a bit.

I'd like to know some tips, exercises and other stuff that could help me to reach some higher notes (up to like A4) without fucking up my vocal cords.

There are a lot of vocal exercises out there to expand range, one that I've been doing lately is starting off with an "ah" as low as you comfortably can go, and smoothly and slowly raise your voice as high as you can. Then do the reverse, start as high as you comfortably can, and then slowly and smoothly lower it. Go back and fourth with this and after a while you should see an increase in range!

Go to YouTube and search for vocal range extension exercises (and resonance exercises, as that'll help a lot with a full sound even in your existing range).

Be consistent with your practice. If you haven't extensively done exercises for range, it will increase quicker than you might expect if you practice regularly. Every time you practice, which should be almost every day, just take 15 minutes or so and dedicate that to your range extension.

I sing along with Jacobs Vocal Academy, but there are plenty of companies and exercises to choose from.

Good luck!