There is a typo. Sorry. Would you mind correcting right things? =>Would you mind choosing correct things?

You can say any of those things. To modify a verb, you need to use an adverb, not an adjective. That would make #2, 4, 6, 8, and 10 the preferred choices. However, the others are not wrong. If you use an adjective, it would modify the implied subject, which is "you", rather than the verb. For example, "Play good!" means to play in such a way that you be good.

Yes it's weird. I watch a lot of boxing, and some other combat sports. They don't like to be called "players", they like to be called "fighters". But even in non combat sports, like football, telling them to be careful is not really done, because they need a very assertive, arguably aggressive attitude for best performance - being too careful spoils their performance. Such a command like "be careful" can also be a bit patronising to a professional sportsman. So, fans are more likely to simply say "good luck" when greeting them before the game. If you absolutely need to say something like "be careful" I would recommend it be "stay sharp" which means be careful but not in a scared way. Something simple & common like "take care" may be sufficient to not undermine the attitude required for aggressive play, and does not sound patronising; but it's a bit cold & disconnected so may not be what you're looking for. If you have more time, consider saying a short prayer with them - something like this: "May God protect you and keep you sharp & focused at all times tonight. Good luck mate!" I know it's a bit longwinded, but I believe this is necessary in order to make the point clear, warm & genuine without sounding patronising. With less time, perhaps choose between "stay sharp" and "good luck" and "take care" depending whether you have an advisory role, or are just a humble fan, or are a loved one.

Americans will say just "good luck" to our friends or opponents. Adults/Parents tell our children to "be careful" when they play.