Can Xbox Support remove some of my games and Achievements?

No, there's no way to have achievements removed.

Sorry, but support gave you some incorrect information. Moderators only police the forums and are not able to remove achievements. Achievements can only be removed if you're given a gamerscore reset which removed every acheivement, not just specific ones.
There is no way to remove specific achievements.

Depending on the game some games achievements change and some are removed

Are you sure that the achievement is obtainable

Hello! I'm a having a little trouble with your question.

Have you found an Xbox Achievement that somehow breaks Xbox's Terms of Service?

7 years ago, I used some cheats in the game for winodws live. I activated some achievements and are now marked by trueachievements because my game number does not meet the conditions for deleting 3 games in 203 games (I only have 70 or so) I only let Microsoft
help me remove those achievements.

If you have cheated and the games removed from your gamerscore there is nothing you can do. You cheated and that is part of the punishment.

There's nothing anyone on the forums can do i'm afraid.

If you were denied a refund after replying to the refund denied email then there's nothing you can do.

I suspect it wasn't just the achievements that was the sole reason but the fact that you had already had a refund for another game not long ago.

Once a achievement is unlocked on a game it can not be removed,not by support or anyone.

The only time it does happen is if the enforcement team find that someone has modded their Gamerscore & then it is only xbox 360 games achievements that are removed as xbox one achievements can't be modded.