Is it possible for two people to carry almost identical genes ...

... but not be related, at all?

Technically, we all carry the same genes.....

So, I'll assume that you are more concerned with the full DNA structure. If you look closely, you will find that the DNA comparison usually carry a probability factor. So, the probability of two people having the same DNA is something in the order of 6 * 10 ^(-10), which means it is possible for two people to not be related and have almost identical "genes", but very unlikely unless they are directly related.

No, it's not possible. If for no other reason, because all humans are related -- so there's no such thing as two people who are not related at all.

I dont think so, they would have to be somewhere related down the line, im sure its possible for very similar but no wear close of identical if they do not have the same parents

mostly monozygtic twins have almost identical genes but note that 99% of the genes found in all the humans are identical.

maybe, but the chances are so small that it would probably never happen, and if it did, there are so many people in the planet that they would never find out

Nope. They could look similar but not have similar genes.

There's always a non-zero probability, but extremely unlikely.