Translation:I want to watch tennis Tuesday morning.
Should this be "...gwylio'r tenis..."?
Or are both forms acceptable?
One Memrise course (supposedly based on Cwrs Mynediad) teaches "gwylio rygbi"; Say Something in Welsh teaches "gwylio'r pêl-droed"; I think I've seen Duolingo teach the version with definite article for sports before as well...
Are both forms (with and without definite article) in use and acceptable?
Do they have a difference in meaning?
For example, "watch tennis" (in general) vs. "watch the tennis" (a particular tournament)?
Yes there is a difference in meaning. "Gwylio'r tenis" would be specifically one particular event of tenis, whereas "Gwylio tenis" is general.
The "response" given by Duolingo says "... watch some tennis ..." Where does the SOME come from?
From how English works.
"some" acts a bit like an indefinite article for uncountable singular nouns and for plural nouns.
Welsh doesn't have indefinitely articles, so when translating from Welsh to English, it's sometimes necessary (or at least possible) to add words that are not a translation of one specific Welsh word.
The other way around, as well, as when you may need to insert words such as yn in a Welsh translation that don't "come from" any word in the English sentence, but are needed because of how Welsh works,