Congratulations on finishing the game, and glad to hear you enjoyed it
In response to your questions (some spoilers):
1) It really depends on how you want to play, but every class can finish the games without using a cross-class skill. Putting points into other skills gives you more flexibility with solutions. Magic can come in handy if you think of the magical solution, and you can also use it in combat provided you have a magic staff equipped.
2) Yes, a warrior can also get the frozen flower. You'll need a certain magic item to help pick it up though.
3) You can get the golden apple if you successfully complete Lithrasir/Liff's quests.
4) Yes, you can retrieve your supply bag. It's probably less straightforward for a warrior, but maybe you have a certain skill which means someone can help you
(and no, I don't mean fast talk).
5) Part of the puzzle with the slider puzzle is actually understanding its function
6) A non-rogue can join the Thieves' Lodge provided she has the thievery skill, I believe.
7) Various NPCs tell you the story of the swanmaiden (Eitri, for one). Basically, Volund took her wings so that she couldn't leave him. Hervor does love Volund and Heime, but she also wishes to be free. And even though she has wings, she can also turn back into human (see the end-credit screens).
8) I believe that your class limits you to which weapons you can equip. E.g. a battle axe is too big for a rogue and a sorceress!
9) The swamp beast is a warrior only quest.
10) We'd always intended for this game to be free, and being free also means that more people would play it and enjoy it. Since we're not making games for a living, we're also not beholden to deadlines, which means we can make the game as best as we can without giving up on quality. However, in the future, we may not be able to get our games onto Steam/other distributors for free, so we hope that some people who enjoyed Heroine's Quest will be open to playing our other games when we release them - even though we're still doing this as a hobby
11) A sequel depends on whether there is enough interest and whether we have enough time to commit to one. We're not ruling it out though; it's just not on our current list at the moment (we've got a number of smaller projects we want to complete first).