really sounds like she is saying "Diom" here instead of Dion!!
Tá an éan é an focal!
(I tried to say 'the bird is the word' lol)
Does díon not lenite because of dentals dots?
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.)
Why isn't díon eclipsed here?
Probably a DeNTaLS DoTS thing again