I did fly a couple of times last year for work around the state, this added to my trip to Vegas has now left me with ~11,000 miles available. So first question, can I use these for anything? Do they expire?
Alaska just introduced 5k-each-way awards on flights under 700 miles, so that could be a one-person round trip if you can find availability. And your miles don't expire as long as you have some kind of account activity, whether burning or earning (including through non-airline partners and the credit card), every two years.
I have accrued ~70,000 miles lifetime, after high school no trips until last year :/ Next question, if I can use those 11K miles, will they be subtracted from my 70K?
Nope--you don't need to save up a million miles at one time to hit Million Miler status. Redeem away.
It sounds like if you do get the credit card approval anytime soon, it'll probably be for the Platinum Plus instead of the Signature--so you'd get two miles per dollar on Alaska purchases instead of three, 5k miles signup bonus instead of 30k, and an annual $50 discount instead of the companion fare. The Signature just won't be doable for you without a co-signer; the Visa Signature minimum credit limit is typically $5k, and even the summer before my senior year of college I only got approved for a couple of $2-2.5k cards while making fairly decent money for a full-time college student.