"Feicim éan ar an díon."
Translation:I see a bird on the roof.
If you speak Ulster Irish, yes. In the other dialects, it would eclipse in this case. However, <d, t> don't eclipse after preposition + singular definite article except in Munster.
Is there a way to say the word "on" without saying "on the"? For example, "I saw you on tv"?
Yes — e.g. “I saw you on holiday” would be Chonaic mé ar saoire. (“On TV” would always be translated with an article — ar an teilifís.)