When I write something like this:
I am a man that is doing these things.
Is it correct to shorten it like this?
I am a man doing these things.
And does it require commas?
When I write something like this:
I am a man that is doing these things.
Is it correct to shorten it like this?
I am a man doing these things.
And does it require commas?
'Who is doing these things?'
'I am the man who is doing these things'
'Who is doing these things?'
'I am the man doing these things'
Depending on the context, we can omit the 'that is'/'who is'. Sometimes this will help to shift the focus/emphasis in the sentence.
They are both grammatical sentences, but the first one sounds a bit awkward. I'd use the second one, which is more natural. No commas are required.
Both sentences are defining (restrictive) relative clauses, so you definitely shouldn't use commas.
The second sentence is a reduced relative clause, so just google 'reduced relative clause' to find out more.
However - "I am a man who/that..."is a bit unnatural - I notice that Kris changed a to the, which sounds much better. The relative clause is defining who you are - you are the man, not just any man.