The only reason OP's example #1 might seem "odd" is because we don't have the full context.
It's effectively meaningless to start a conversation or text with but, because this particular "contrastive conjunction" almost always applies to something previously mentioned. Thus, sentence #1 is perfectly natural as a response in the following...
"You should have told me you had Aids when we first met!"
"But I didn't know that then, although I learned it later and have been meaning to tell you for a while"
...where but contrasts with the preceding utterance by the other speaker, and although contrasts with the first part of the second speaker's utterance.
In OP's example #2, again, but contrasts with the preceding statement. But in this case, both the elements being contrasted by although come after the conjunction.
It's just about possible to start a "conversation/text" with but (you open the door to someone you weren't expecting to see, and exclaim "But what are you doing here?"), but that's an unusual/poetic/dated usage. In general, but always applies to something previously specified, whereas although can optionally be moved before its referent...
"My dog likes chocolate although it could kill him if he eats too much" 1
...is equivalent to...
"Although my dog likes chocolate it could kill him if he eats too much"
Hopefully that shows how although can be placed in different positions. And if a previous speaker had said "Any animal instinctively knows and seeks out the food its body needs to remain healthy", either of those last two examples could be preceded by but (introducing a refutation).
1 In this (but not the following) example, either conjunction works...
"My dog likes chocolate but it could kill him if he eats too much"