Hi Bush3102,
Yes, you can do all three, but you will need to either write some code or use one of the InfoPath accelerators out there - for example: qRules and/or DBXL. InfoPath 2010 list forms do not support sending to 2007 lists without code and vice versa with 2007 form library forms. Form library forms can connect directly to a database, but Web services are a best practice sine they create a middle-tier which provides greater flexibility when things change. qRules supports mapping your InfoPath form to both a 2007 and a 2010 list and there are videos that show how to do that (for example: http://www.youtube.com/watch?v=mpueygXbV-A&feature=player_embedded). DBXL is a Web service that will connect your form to a database (for example: http://www.youtube.com/watch?v=nPhyS2CtScc).
Free trials of both "accelerators" exist on the Qdabra dot com web site. And, the tools are very inexpensive to buy.
Disclaimer: this web site is a free resource to the InfoPath community. Qdabra pays for it's annual maintenance and guarantees responses to most of the threads.