When was the last time you've had a haircut?

Alternatively:
"When was the last time you got a haircut?"

I hadgot a haircut two weeks ago.

Unlike in the title, it DOES NOT make sense to say
"I HAVE had a haircut."

I don't have a proper explanation for why this is. ごめんなさい。

I dohaven't liked bangs from a young age because they are tickledish, so my hairstyle has basically has been short.

"from a young age" is in the past tense, but "I don't like" is present tense.

"bangs are tickled" means "the bangs got tickled," instead of "the bangs do the tickling"

Also, I’ve never dyed my hair in my life.

There are some people that changinge their hairstyle frequently, but areisn't theyat troublesome?

aren't they troublesome = あの人は迷惑じゃない？

"they" is for living things, and "that" is for non-living things.

From a young age, I doidn't like bangs from young age because they are tickled, sohaving bangs, because I find them ticklish. So basically, my hairstyle bhasically ha always been short.

1. You can replace "I find them ticklish" with "they tickle me", if you want.
2. For the second sentence, you can also say "I have always kept my hair short."

Also, I’'ve never dyed my hair in my entire life.

There are some people who frequently changinge their hairstyle frequently, but areisn't theyat troublesome?

I dohaven't liked bangs from a young age because they are tickled, so my hairstyle bhasically has generally been short.

"they are tickled" implies that someone else is carrying out the action of tickling upon the bangs
Instead of "basically", "generally" is a more natural word choice here, and it usually comes after "has"

There are some people who changinge their hairstyle frequently, but areisn't they troublesomeat a pain?

"aren't they troublesome" sounds like you're criticising those people for causing trouble. I think you intended to ask if it's not a pain to change your hairstyle often