"Where is a swimming pool?"
Hm... I'm not sure what exactly you need, it's such a broad question.
If you need an overview of all the possible endings, you could use Wikipedia, for example: https://en.wikipedia.org/wiki/Ukrainian_grammar#Nouns
However, this might be too advanced. This course is expected to teach you this in bite-sized chunks, so maybe you just try to learn them in context and ask specific questions about certain sentences?
As for this sentence, the «байссейн» here is in Nominative case, since it's a subject of the sentence. Masculine nouns usually end in a consonant in Nominative case (however, some nouns don’t, like ба́тько 'father'), and -й is considered a consonant in this case. However, when й is followed by a vowel, we don’t use й, instead we use another letter: йа is written я, йе = є, йі = ї, йу = ю (йо doesn't change), so this might be confusing.