I think the fact that you have a couple of Tickets ( Traffic?) should not affect wether or not you get a VISA for another country, My first advise is to pay the tickets to get them out'a the way, because when you get back, those tickets may turn into warrents??? If you really nervous about spending the $$$, contact a para-legal and get them to look into it for you, they should be able to tell you the law when it applies to state or county violations and international visa's. The part about asking for your plane ticket, i am going to guess, is the wanna make sure your going home, as much as you love the country your going to and they love you as a tourist, they don't want you to make it your home...not unless you have big $$$, then they would welcome you with open arms for as long as you want!!!
Hope that helps some dude!! B)