Two-Cat Household

I have had Johnny (2.5 y/o male, neutered) for about 2 years. He came from a shelter, but was the only cat in my apartment until about a week ago. Cid (4-6 y/o female, spayed) came from the same shelter.

Unfortunately, I did not introduce them properly. Half of it was from ignorance of not researching on how to bring a new cat into the home, the other half was that I do not have enough space to have a "safe" room to keep them separated.

At first, Johnny was ticked off that I brought another cat home. Cid mostly hid under the bed. They are at the "I don't like you, but I shall tolerate you" phase, which is fine by me. I totally understand that my cats may never be best friends.

What I don't understand is that for the past two or three nights, Johnny has gotten in this mood where he will go after Cid. He'll run up behind her and pounce. I don't think that he's trying to mount her. The part that worries me is that he doesn't let up. Cid will end up on her back, hissing, and claws out at Johnny. She'll run, but Johnny will continue to stalk her for a few minutes. And then they're fine. Only once in these last few nights has Cid been so distressed that she tried to run away and get up the cat tower, but almost fell off from being so crazed.

Can anyone give me some input as to whether they are fighting or playing? Also, are there any other steps that I can take to make the acclimation of the cats easier (both on them and on me)?

Thanks!

It just drives me nuts that they are sniffing at each other, nose-to-nose one minute, then playing/fighting the next!

The thing that confuses me is that the fighting/playing is not occuring at all times. Like tonight, I had one cat on each end of the couch, sleeping peacefully.

If I do separate them, and put Cid in a safe room, won't she be distressed because she has already explored the rest of the apartment? It doesn't seem "fair."