- The infinitive of vill is (att) vilja and it is indeed irregular. In Swedish we often list the conjugations infinitive, preterite and supine of a verb and call them the "theme" of the verb. For vilja, the "theme" is vilja, ville, velat. Here are all its conjugations: http://sv.bab.la/verb/svensk/vilja
- Vilja does not imply that you want ownership of something, as it does in English or French. In English if you want to do something, you use "want to" + verb. In Swedish this is the only valid construction, but without the "to" (would have been att in this case) so the construction is the same if you want to ride, you want to work or you want to have something. Therefore, to want something = att vilja ha någonting; to want to do something = att vilja göra någonting. I hope I didn't make it even more confusing.
It's like in a restaurant when you tell the waiter, "I will have the steak" aka "I want the steak." I think we really only use "will have" to mean "want" in terms of choosing food/drink options in English. I can't think of any other times at the moment. But it would still be slightly more polite to say, "I would like..."