1. U need to make phone calls and research online and c the best offer
2. Yes you can accumulate ur miles. Don't need to own a credit card. For
delta, their loyalty program is Sky miles, just go and register an account
for free, and you will begin earning miles.
If you have any kind of credit card, you can earn cash back or miles, etc
3. Keep your SkyMiles number with you. If you order ur ticket online, there
will be somewhere asking ur SkyMiles number, if u call an agent, tell them u
wanna Delta and see if you can give them ur SkyMiles number.Some of the
agents accept, some don't coz they benefit with their own loyalty program.
For some of the airlines, u can accumulate ur miles when u check in. Not
sure about delta