Sure you can it's called cash.
car max
There are actually plenty of alternatives. You can buy a home, buy a car, even some home utulities services will do it depending on where you live. Typically, if they ask for you SSN, then it will most likely appear on you credit report.
You can check to see if your credit is good enough to buy a car by filling an application. There are many car dealers and finance companies that will finance your purchase regardless of your credit score so everyone can buy a new car.
yes
No
start building your credit, get a department store credit card, like a target card, buy stuff then pay it off the next day.
save up
Yes, but you have to buy it straight out and you can't drive it on the road! Buying a car on credit, you need a valid Driver License in order to get Insurance. A car dealer wont release a car on credit without proof of insurance and Insurance companies won't give you coverage unless you have a valid Driver License.
Without any credit? Probably not at a reputable dealership without a co-signer. Probably yes at a shady used-car lot, but they will charge you outrageous interest and will vastly overprice the car you are buying and underprice your trade-in. If you are buying your used car with cash, yes. If you're going to need an auto-loan it will be very difficult or impossible with no credit. You can certainly sign up for a credit card with no credit and use it to build your credit. That process may take some time. If a co-signer is available for you to use you'll have a better chance than with no credit. Without either it will be nearly impossible.
Yes.
money
At the moment the only way to buy apps is with a credit card.