"Do you see this?"
Why is "to" used here and not "ten" or "ta"? I am assuming that it is because, since the object is unknown, you use neutral gender? I just want to clarify.
It's a little tricky. To use "go" or "ją" (as ngfio mentioned), the object must be either animate (so animals are also cool), or the person you are talking to must already know what object they should look at. So even if you know what it is that you want to bring attention to, you can't just use "go/ją" out of the blue at unexpecting person.
If, for example, you asked somebody else to help you look for something specific (and let's say you lifted a heavy sofa and the other person is then supposed to look underneath), then you should use appropriate gendered pronouns.
As a final note: you are supposed to use accusative case, so it's go/ją, not ten/ta. "To" just happens to be identical in both nominative and accusative.
You use "to" because you are referring to a thing (or a situation). If you were referring to a person you would say "[Ten chłopiec.] Widzisz go?" = "[This boy.] Do you see him?" or "[Ta dziewczynka.] Widzisz ją?" = "[This girl.] Do you see her?" (and in plural it would be respectively "ich/je").
You can't say "Widzisz ten?" or ''Widzisz ta?'' even if object is known. You always have to say ''Widzisz to?''
The short answer is that to is used as a noun. When it's used as a noun determiner, then it's to for a gender neuter noun, ten for a masculine, and ta for a feminine noun.
I said "Czy widzisz to?" and was marked wrong. It said it should be "Widzisz to?" Is there any reason not to use "czy"?
"to" is a pronoun, and it really is best to avoid putting pronouns at the end of the sentence, if other word orders are possible.
Yes, it is. It is a longer form - skipping "czy" is quite usual in casual speach.
Is 'czy to widzisz' ok? I remember reading that 'to' should be avoided at the end of a sentence unless doing so put it at the beginning.
Yes, that sounds ok and is accepted. But I'd probably go either with "Widzisz to?" or "Czy ty to widzisz?" (which is more like disbelief - you see something so strange you actually want to make sure if it's not just your imagination).