The problem here is that in British English as in Welsh we'd say "Have you had a bath yet?" i.e. the perfect tense. What's translated as "Did you have a bath?" is formed in a different way in Welsh i.e. the simple past, and wouldn't be used in this sentence either.
So although you're correct, it's best to think of this as "Have you had" and you'll learn "Did you have" later in the course. Otherwise you might get into confusion.
Nevertheless, teaching things wrong is always going to confuse people more. Sooner or later you have to teach people that the "elasticity" of a tense in English will not always be identical to that of its nearest equivalent in Welsh (or any other language). I go for sooner rather than later. However, teaching people that there's a mysterious difference between the past simple and present perfect simple in English in this context is clearly no way to focus on the target language.
Yep, the past tenses (perfect, simple past, imperfect, pluperfect) are usually used in exactly the same in Welsh as they are in British English, so for most learners it's not an issue. American English sometimes has slightly different usage so this is where this particular problem arises and where American learners need to pay attention to the differences found in Welsh.
I don't know that I've seen a list. That said, cael can be used with:
receiving, getting, catching e.g. cael llythyr "have/get a letter", cael anrheg "have/get a present", cael newyddion "have/get news", cael pen tost "have/get a headache", cael syniad "have/get an idea", cael anaf "have/get an injury"
food and drink e.g. cael coffi "have a coffee", cael brecwast "have breakfast", cael brechdan "have a sandwich", cael peint "have a pint"
times and events e.g. cael amser da "have a good time", cael hoe "have a break", cael gwyliau "have a holiday", cael parti "have a party", cael dosbarth "have a class"
baths and showers e.g. cael bàth "have a bath", cael cawod "have a shower"
giving birth e.g. cael babi "have/having a baby", cael gefeilliaid "have/having twins", cael cathod bach "have kittens"
talking and chatting e.g. cael sgwrs "have a chat", cael gair "have a word"
Doing the Past Cael lesson again, I see as objects of verb cael: syndod (surprise), anrheg (present), ffôn symydol, car, so it's not just baths and food, could perhaps be anything that you would buy. I need to keep better notes. Cael amser da surprises me; thought it would be idiomatic and not translate straight.
"Have you had another bath" would be Dych chi wedi cael bath arall?. Oes gafr eto is, I guess, an older usage of eto and the literal English translation "Is there yet a goat" gives you a clearer idea of how it sounds in Welsh too. Using eto like this isn't really done in the modern Welsh Duolingo teaches.