I brarely saw him make any mistake. I rarely saw him make a mistake.

Could also be "saw him make any mistakes" but what I wrote is most natural.

I barely saw him make any mistakes. I barely saw him make any mistakes.

plural is needed

4) Stop doing that.! 4) Stop doing that!

Exclamation point works better at the end to indicate your strength of feeling.

You're gonna scupper our plan.! You're gonna scupper our plan!

Scupper is not a super common word but the meaning is fine. A more common phrasing might be "You're gonna mess up our plan!" or "You'll ruin our plan!"

5) If you want to knowfind the real of this city, go visit the ghettos/slum(need a noun here) of this city, go to the poorest areas. 5) If you want to find the real (need a noun here) of this city, go to the poorest areas.

Real here is an adjective so you would need a noun it describes - "the real personality", "the real heart", "the real flavor", etc. And just "know" here is vague. You would want "to get to know", to "learn about", or "to find".

1) My brother and I resemble in appearanceeach other. 1) My brother and I resemble each other.

The verb resemble requires an object - you have to resemble something. In this case, it's each other. "In appearance" is unnecessary as resemble means "to appear like".

1) My brother and I resemble ineach other/ look alike/ have a similar appearance. 1) My brother and I resemble each other/ look alike/ have a similar appearance

To resemble one another, implies that you are referring to appearance. There are many ways you can phrase this, I listed a few.

2) There were some personnel changes after the new leader was induappointed (elected.?) 2) There were some personnel changes after the new leader was appointed (elected?)

Inducted tends to refer to entry into an organization, but you seem to mean a person put into a new job role.