I still have a few doubts about these sentences. I really hope you can have a look at them.

I like wearing casual clothes and also sports clothes. (corrections: and sports clothes too/ as well as sports clothes)
2) I'm holding/carrying a hiking pole (stick?) im my right hand.
3)I've never been in/to (but not at?) the new supermarket yet.
4)I've never flown in (not "on")a helicopter. I don't like wearing too coloured (bright) clothes because I don' want people to watch me.
5) How long go did you arrive? How long is it since you arrived?
6) I think these clothes are the most popular among teenagers. (and not: "for teenagers").
7) I'm wearing black-and-white trainers (also two-color trainers).
8) I've never been to Mexico so far, up to now (but not: "till now")
9) Have you beem there yet? No, I haven't been there yet.
(or: No, not yet. What about: No, I haven't been yet?)

Sure, let's go through your doubts and make the necessary corrections:

1) I like wearing casual clothes and also sports clothes. (corrections: "and sports clothes too" or "as well as sports clothes") - Both corrections are acceptable and convey the same meaning. You can use "too" or "as well as" to indicate that you like wearing sports clothes in addition to casual clothes.

2) I'm holding/carrying a hiking pole (stick?) in my right hand. - Both "hiking pole" and "stick" can be used interchangeably in this context to convey the same meaning. You can use either term based on your personal preference.

3) I've never been to the new supermarket yet. - "I've never been to" is the correct phrase to use when expressing that you haven't visited a place before. "Been in" or "been at" are not appropriate in this context.

4) I've never flown in a helicopter. I don't like wearing brightly colored clothes because I don't want people to notice me. - "Flown in" is the correct phrase to use when referring to traveling in a helicopter. Also, it's more appropriate to use "brightly colored" instead of "too colored" to describe clothes that have vibrant colors.

5) How long ago did you arrive? How long has it been since you arrived? - "How long ago" and "how long has it been since" are both correct ways to ask about the time that has passed since someone arrived. Both versions are acceptable, but the second option is more common in formal English.

6) I think these clothes are the most popular among teenagers. - "The most popular among teenagers" is the appropriate phrase to use when describing clothes that are favored by teenagers. Using "for teenagers" would imply that the clothes are specifically designed for teenagers.

7) I'm wearing black-and-white trainers (also called two-color trainers). - Both "black-and-white trainers" and "two-color trainers" accurately describe trainers that have both black and white colors.

8) I've never been to Mexico so far, up to now (but not: "till now") - "So far" and "up to now" are appropriate phrases to indicate that you haven't been to Mexico yet. "Till now" is not incorrect, but it is less commonly used in this context.

9) Have you been there yet? No, I haven't been there yet. (or: No, not yet. What about: No, I haven't been yet?) - "No, I haven't been there yet." and "No, not yet." are both correct ways to negate the question. "No, I haven't been yet." is also a valid response, but it is less common to omit the word "there" in this context.