You're welcome

Bir şey değil

"gibi" means: like, as, same as.

if you say "senin gibi" it means "like you", "same as you"

senin gibi yapıyorum: I'm doing it same as you/like you.

Ah, another adjustment:

"şey" is a noun and should be written apart all the time.
Herşey --> Her şey, birşey --> bir şey, etc.

Only you should put "gibi" after "senin"
And no need to change in this sentence. Perfect

Bir şey değil.

The difference between these two, seni mutlu etmek/senin mutlu olman, is that

mutlu etmek: to make you happy, because I make you happy
mutlu olman: being happy, because you will be happy

And I also want to clarify this:

when we say "gittiğin yer"(a place that you went) "gittiğin" will be an adjective in the sentence.

when we say "gittiğini gördüm"(I saw that he's gone) "gittiğini" will be an object in the sentence.

A little hint: If there is a suffix(-i, -ı, -u, -ü etc.) after these types of words, it is not an adjective. As you can see above.