You're not going to love my answers, sorry in advance.
Nope. You're going to have to finance it yourself. You may be able to get some scholarships, but other than that you are on your own. Some regional airlines offer programs through Part 141 Universities to hire you your junior year, then have you instruct until you reach the required time.
Read more into the rule. ATP is 1500 hours unless you go to a school with a waiver. Your regular everyday flight school is NOT a Part 141 school, but Part 61. If you don't have classroom instruction with a set TCO, you are in a Part 61. If you want to save money, I recommend looking into a Part 141.
No, it's not like a bid sheet goes up and you get a FT Pilot Bid.
You've gotta look into good flight schools and save your money. But you also have to remember things are going to be tough for a while after you get all your licenses. I'm sitting on 65,000 in debt for flight fees alone. I have my Commercial multi engine license, and a CRJ type rating.
There's a reason I'm a FT ORS and not a pilot. I would have taken a pay cut going from being a PT Sup to a FT Pilot. If you love aviation that is great, I do too. But you have to realize it isn't as great as they make it out to be. Do you eventually end up sitting pretty? Absolutely, but these days the investment costs are very high. To get hired at UPS as a pilot is very difficult too. You need 3500 hours total time, usually at LEAST 1500 turbine. Doing right seat in a Cessna as a flight instructor doesn't get you that. To get the turbine time you'll either need to fly for a regional or a small feeder operation. Even then though, it's tough to get on the list.