Yes, that's fine. Look up "alternating dumbell curls" for one way to do it. But you can always do one arm, then the next arm.
Not really. You'll probably get some out of doing one-arm rows for awhile, but it's really not enough.
Take a look at inverted rows. You can use a broomstick over a countertop or chairs, or do them underneath a table with your hands on the edge.
There are also removable indoor pullup bars that go over doorways; that's probably your best bet as far as working up to doing pullups without going to a gym.
Really, this can be all over the place.
When you're talking about "back", it's really a couple different areas that ought to be addressed.
- You have your spinal erectors, which basically do the opposite of your abs, and help you "unroll" your back after touching your toes. They also keep your spine properly lined up. Deadlift variations are a good way to hit these; you can look into one leg romanian deadlifts, although you don't really have enough weight.
You have your lats, which run down both sides of your spine and give people that V shape. (There are also a couple other muscles that contribute to this too). They help pull the arms down, and along with the spinal erectors, keep your spine in line. From the back, the spine and shoulders make a T; the spinal erectors run along the vertical part, and the lats connect the top corners to the bottom point (and fill in all the rest of that space). Pullups and pulldowns are good for hitting the lats.
You have your "upper back", which consists of a few different muscles, but this is the area almost exactly opposite of your chest, and mostly is responsible for keeping your shoulder blades in place. This is probably the most important part to keep balanced with your pushups. Inverted and regular rows area good way to hit this.
In addition to those, you have your glutes and hamstrings, which aren't your back, but are still part of your "posterior chain", i.e., the back side of your body. There are many benefits to strengthening those too, but I'm not sure how to do that with the equipment you have.
I don't know if that made things easier or more confusing, but for now I think you should work on inverted rows, and then get to the point of being able to do pullups.