Is my sentence below, grammatically correct?

It's a sentence fragment but beyond that I would need to know what you're trying to say. 

No one is mentioning how the question is also not grammatically correct. There shouldn't be a random comma between below and grammatically

In simple terms, you don't have a sentence. There is no verb.

So, maybe something like:

"The best participant had ten entries."

Your "sentence" contains no verb, so it is not a sentence at all.

The sentence doesn't seem right ; and adding an 's' could worsen it for me   

'The greatest participation, with 10 entries' is what I would write

The phrase is incomplete as it is not qualified. 'Most' is either a determiner, a pronoun, or an adverb. So it could say:-

'The Red Team displayed the most participation with 10 entries.' However 'most' is not a good choice. Perhaps 'The Red Team displayed the greatest participation with 10 entries.'

I would add with "a total" of 10 entries.forget the s.

The verb is missing.

He won the contest as he had the most participation with 10 entries.

No, sorry, it is very incomplete. 

What is it that you are talking about?

The most participation out of how many events? From how many years?

How many could enter the competition total?

You could say something like:

We had the most participation this year for the baking contest than we have ever had, with all ten slots filled with entries.

It isn't actually 'wrong', but I would write it as:

The greatest participation, with 10 entries.