I bought this to use while travelling: http://www.amazon.com/LifelineUSA-4-PCU-Lifeline-Power-Chin-Up/dp/B006PDK1B4/ref=sr_1_12?ie=UTF8&qid=1423258099&sr=8-12&keywords=door+pullup+handle
It's seemed to work well so far. I tied a rope between the two and can do one-arm rows by only putting one over the door and holding onto the other one.
I don't think there are any good alternatives to pull ups. If you can't get a bar, you can get some straps that will hang over any three hinge door, but pull ups are a must. (Sorry, I know they're out of stock on that link but your local sport/fitness store may carry something similar).
As for the bench, the only excercises there that require it are the split squat and the bench press. You can do a floor press instead and use a chair in its place for the split squat. Do the shoulder press standing. I'll disclaim though that the floor press will not be nearly as effective as a bench press.
If it's a money issue with the bench, you can get a cheap one for as low as $50, or search craigslist for people who are dumping fitness gear for cheap or even free. Alternatively, if it's a space issue, I recommend this bench, which will collapse to slide under a bed or fit in your closet.