^ You're welcome~
ずっと気が合う気がしてた
似た者同士でやすらいで hey
好きなものも嫌いなものも同じで
Only you save me
I always felt like we'd get along
We're two peas in a pod, I feel at ease with you, hey
We both like and hate the same things
Only you save me
I guess the two ki's can be confusing

They're both set phrases:
気が合う (ki ga au) = to get along well with someone; to hit it off with someone
[...]気がする (ki ga suru) = to have the feeling that […]; to feel that/like [...]
似た者同士 = people who are alike/similar; people who are like two peas in a pod. (it's a combination of 似た者 (nitamono; people who are similar) and 同士 (doushi; companion)
安らぐ (yasuragu) = to feel at ease; to feel secure
I'm not 100% sure about the 'yasuraide' part either. I think it's the -te form of the verb 'yasuragu' and it's meant like 'the fact that we're so similar makes me feel at ease.'
世界を君が疑っても
私だけ ただ信じて
'Even if you distrust the world
Trust only me'
It's like you said.
'utagau' = to distrust something or someone'. The 'something' is 世界(sekai) because it carries the 'を (wo)' particle. Lyrics tend to drop particles but technically 私だけ(watashi dake) should also be followed by を (wo).