Question is she would be going in as an officer and i would be enlisted, is this a problem?
As long as you are married before you enlist, it is allowed - assuming that's the 'problem' to which you are referring.
Also are there anyway living arrangements could be made for both of us once she gets to "A" school?
Officers don't go to A-school. Her first stop, if she gets selected as a nuke, is either her first ship (SWO) or power school (subs). It's a permanent change of station (PCS) move, so if you are married then the Navy will also move your belongings with her. The housing on Charleston when I was there was reserved for people with children, and as a couple with no kids you will almost always find a better deal renting an apartment in town anyway.
If you are not married yet, she will definitely have to find housing in town. You can move in with her if you wish, no one will stop you. But no one in the Navy will help move your stuff, either.
And lastly when i'm out on deployment I would be leaving without her? Is that correct?
You cannot be stationed on the same ship as your spouse, so you would always deploy without her.
Basically we're both going into the same field, and i'm just trying to understand how, if at all, we can stay close?
Google 'milpersman' and 'dual military couple.' It will outline what the military will do. The cliffnotes are that they will attempt to assign you two to the same duty station within reason. This will be easier if you are both subs or both surface, but much more difficult if one of you is subs and the other is surface. Also, junior officers PCS more frequently than junior enlisted Sailors. She will head to her shore duty while you are still assigned to a ship, and as an enlisted nuke your shore duties are almost assuredly going to be prototype or prototype, while she will be assigned to various staff jobs to get experience with Big Navy. Since it's more likely than not that your shore duty timings will not align, you will have to be prepared to be stationed in a different location than her for a significant period of time.
Keep in mind that you could get the bonus of being assigned the same duty station, but on opposite deployment rotations (e.g. she is on deployment from March Through December, but you are on deployment Jan through June, at which point she leaves for a training underway, etc. etc.).
Your life gets much more complicated with children, there are also provisions in the milpersman for how the Navy handles that.
My advice would be that if you are not "100%, gung-ho, this is the only thing I can possibly imagine doing" about enlisting when you have a military spouse, then don't.