A note is made of your passport expiry date, so immigration is aware of it. I have a passport sticker, the date is written on it of my passport expiry date ending before my DTV. I guess those with a PDF DTV a note is made on it too, When you get your new passport, carry your old one with you.
Sponsorship rules vary depending on the embassy you apply from. It can be easier as many do, to 'borrow' the money from your father to deposit in your account and apply yourself.