Both tills and till are acceptable in this sense before a noun, but it isn't recommended to use till this way to start a subclause.
till i morgon and tills i morgon both work, but only Vi håller på tills imorgon 'We're keeping at it until tomorrow'. (or like here, tills frukosten kommer)
The general idea behind Duo is that you're supposed to learn like children learn – by seeing lots of examples. Clearly that isn't enough, and we do try to give some explanations, but the use of prepositions is very hard to explain concisely, and the cluster till, åt, and för are among the hardest ones.
When it comes to till frukost 'for breakfast' I'd say it's just a set expression so that in reality there's really no point in trying to analyze it, although some of us can't resist trying to do so anyway, which is why I mentioned the 'purpose/goal' examples. One could also analyze it as the 'addition' meaning that till sometimes has.
Below just a VERY short version of the most typical uses of till vs för
till is most typically used
1) with movement to a goal jag åker till Kina 'I am going to China'
2) when giving something to someone jag ger en bok till mamma 'I am giving a book to my mom' – same with jag köper en bok till mamma 'I am buying a book for mom'
för is most typically used
1) whenever there's an 'audience': jag berättade för honom 'I told him', jag sjöng för henne 'I sang to her', jag visade den för honom 'I showed it to him'
2) in 'exchange' situations: jag ger dig 10 kronor för den 'I'll give you SEK10 for it'
3) 'concerning' det är svårt för oss 'it's difficult for us'
There are tons of other more special uses, but if you want an overview to start with, I think you should keep these concepts in mind, and try to build from these.