Nice to meet you!

I have been studying English for about half a year.

or It's been about half a year since I started studying English.

I love fashion, music, flower, cats and taking photos.

and cat!!

I would like to make friends with people all over the world!

I have started to study been studying English for about half a year.

"Start" means "to begin" and it does not work in this sentence because you say that you have already studied English for half a year, which does not make any sense. You could say, "I started studying English six months (half a year) ago." It sounds weird to me saying, "I started studying English half a year ago". I'm from the States and I do not use the term "half a year" quite often, I normally say, "six months ago". Normally, I see "half year" used when describing how long someone has been in a relationship for. For example, "I have been dating my boyfriend for one and a half year."

Sorry, I am rambling, hopefully that didn't cause any confusion.

I love fashion, music, flower, taking photos...

Do not forget to put the spaces!

and cats!!

You would make the word plural (cats) instead of singular (cat) because you like more than one cat!

I would like to be a friends with world people around the world!

"World people" is not a set of words you would use, instead you would say "people around the world". It makes more sense to say this. This would change "to be a friend" to "to be friends" so the sentence is more clearer.

I would like to make friends with people from around the world!

You can say "I would like to make friends with people from all over the world."
Need to say "from."

I love fashion, music, flowers and taking photos, amongst other things.