When I try to play faster things on the bass, my picking hand starts to get tense. Is this normal for a beginner and will just get better when I gain strength, or is my technique wrong?
That happens to beginners, from what I've found. Like jazzy said, relax your hand. It'll get easier with time.
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relax! speed is a byproduct of accuracy. pain is a side effect of trying to play too fast too early.

so work on your accuracy
Oh, and also should I use my third finger to press intervals of two frets?
Cuz I have been using my pinky.
Unless you have really small hands, you should be using the one finger per fret method. Its going to seem awkward at first, but overtime it becomes easier and you gain speed.

Get a metronome and practice first at a slow speed and then increase when you can play something correctly with good tone five times in a row. Then up the speed and begin again.

Good luck and yes, it does get easier over time.
i find if im playing certain runs at high speed, i tend to use my pinky more. but i got a super strong pinky, lol.

it is alot better if you use one finger per fret. this helps strengthen your fingers equally, instead of having 3 strong fingers and a weak one
Oh man, yeah, unfortunately my left pinky does this weird thing where it bends way easier at the big knuckle than at the little knuckle. Just my left pinky. Not that the little one's hard to bend, it's just that the big knuckle naturally just like snaps to a 90 degree angle. Annoying as hell.

And if anything, I use it too much, overcompensating because I don't want to overstrengthen my ring finger. So like Damien said, work on all of them. If I can, you can.
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