Er... I'm quite familiar with RPG's in general, but pretty new to Anima: Beyond Fantasy.

So I'm not entirely sure if the GM is doing it wrong or it's just the game, since I'm so new to this one.

I made one character that had 135 HP lvl. 1 that was one-shoted in his first round of combat. Had 100 attack, 80 dodge.

Then I made another character that had 110 HP, lvl. 1 that had 80 attack and 80 dodge. First time in combat (2nd session in) was put into a state of "fear", then was surprised every round even though I took danger sense, then my armor wasn't working, then was one-shoted...

Now according to him each time the enemies were level 0. I have no idea on this one. Any advice from more experienced people with this RPG?

Things like charm, unlucky, or your danger sense are very GM dependent and it's not uncommon for GM's to ahem be a bit overzealous. It's usually better to stick to advantages/disadvantages that have actual in game effects that are described. That being said combat is also known to be particularily dangerous in anima so he may not have done anything wrong and unless your one of the warrior classes that depends on block, basically warrior, paladin,dark paladin, or weaponmaster, your armor won't be heavy and won't do much. Also as for armor it protects differently depending on the attack types which are cut thrust impact cold heat and energy. The first three are usually well covered by metal armors although thrust is sometimes weaker, the last three tend to be harder to protect against with furs being better vs cold/heat. Without having seen the battle firsthand it's really hard to say what happened.

Your group might need a weaponmaster if your the only fighter. Or one of the nonmagical paladin variants, or a warrior would work too I guess.

The fear state is just plain nasty considering that it gives a -60 all action penalty. (I don't think a level 0 should be capable of putting a character in that state unless you have a phobia to the thing and even then it seems a little harsh but I don't know what the campaign is like)

Really though if you feel there's a problem with balance you need to talk to the DM alone about it. (In a non-confrontational manner of course) Since ultimately as far as tabletop games go, the GM is God.