Military wife here. Quick back story is similar to yours; immediate connection, short courtship (2 years of dating on the weekends with a 9 month deployment in the middle. A 10 month deployment 2 months after marriage and moved across country 2 months after he came home) Relying 100% on him to act as my security blanket, my BFF, my family and friends was tough on both of us. I sympathize with you both, it's a tough road.
As for your issues: Money - Do a budget. You make money? You keep some, and you put the rest in the joint account. Same for her. The bills are paid out of the joint account. It's up to you both to make sure there is enough in there for the bills and one of you is responsible for making sure they get paid. You have to have your own budget to play with, otherwise this resentment starts brewing. Jealousy - it's gunna happen. See a therapist together to get the truth out and figure out what needs to be done to alleviate the distrust (you staying off those damn sites and asking her for more sexy time, or spooning. Whatever it is you need. You said the first time you did it it was because you weren't sure you wanted this serious of a relationship, and then you said another time it was because you were being ignored. What you are craving changes and it's not until you figure it out that you can expect it from her) Communication - this is our problem, and I don't know what to say. We have monthly "board meetings" to discuss issues, concerns, plans, expectations etc to stay on the same page, bUT are constantly working on our day to day emotional communication. See a therapist?
You've got a lot to deal with being in the military, and it won't work without honesty and trust. And those are battles that must be waged daily. I wish you the best, and hate to be negative, but sometimes it's good to have that horrible discussion inside your head to make sure this is what you WANT, otherwise, you could be just doing it because it's what you're supposed to be doing, and end up self-sabotaging everything.
*note I am not a licensed professional in any capacity and just giving advice on what's worked for me, the same things I'd say to a friend.