Three months, especially with a preemie is really early to be expecting them to not be hungry through the night. Even with my son on solids, he was still hungry at least until 12 months at night.
I know that returning to work will be hard with having to get up, but you will just have to adjust accordingly. I would suggest going to bed earlier, making sure that you nap whenever possible (like on the weekends) and if you have a spouse or partner, engage them in helping at night (obviously if you don't, this won't work).
Three month olds are just starting to come out of their shell. You aren't going to really be able to expect a routine at all at this point. ANd if you do, it's just going to change again and frustrate you. Actually, my 22 month old is just now really adjusting to going to bed at a certain time and waking up only once a night for water. You're in it for the long haul. Go with the flow, some nights will be good, others will be bad. When you look back at these times, you won't remember how hard they were, you'll only remember your precious baby.
As far as moving baby to his own room, I would also recommend keeping baby in your room with you a little longer. DS still sleeps with us. It's SO much easier than walking into the next room in the middle of the night and having to really get up. There is nothing wrong with having your baby in your room with you at night. They will probably not be sleeping in there once they're ten years old and definitely won't be in there when they're 18, so just make it easier on yourself and let him stay for a while so you can get more sleep.
I also would NOT recommend giving solids in an attempt to sleep better. Solids should not be introduced until at least 6 months due to allergies forming when babes are introduced early.
I always encourage an active response to a baby. Remember that his only effective means of communicating his needs with you is crying. He was attached to you for 9 months inside of you and even now, he's just starting to get used to being outside of you. Attending to him quickly at night will encourage him that you are there and that he is not alone. He is not yet able to quiet himself and self-soothe. He's still so young.
I know it's hard, mama. Every mother in time has been through this and has had doubts about their abilities to parent and has struggled through those really hard hard nights.
hugs,
Jen D.