Learn Polish: Jestem tu.

In Polish, you can usually leave out the subject pronoun (like ja for 'I') because the verb itself tells you who is doing the action. The word jestem specifically means 'I am', so adding ja isn't needed unless you want to add special emphasis.

Can I say 'Ja jestem tu' instead?

Yes, you can! It is perfectly correct. However, a native Polish speaker would usually just say Jestem tu because it sounds more natural. You would only use Ja jestem tu if you really wanted to stress that I am here, as opposed to someone else.

Does jestem change depending on who I am talking to?

No, jestem is strictly the 'I' form of the verb być (to be). It always means 'I am'. If you want to talk about someone else, like saying 'you are', you have to use a different form of the verb, which is jesteś.

I've also seen the word tutaj. What is the difference between tu and tutaj?

Tu and tutaj both mean 'here' and can be used interchangeably in almost all situations. Tu is just a shorter, very common version.