How many straps are included?

Three, but I need to connect two of them to make it long enough to go around the bra straps.. It's hard to do yourself but soooo nice not to have your straps falling off your shoulders.

can this be used with a bra that doesn't have removable straps?

These bra holders have a hook on one side and the elastic is folded over on the other side for the hook t go through. (The elastic has good recovery.) They are used to pull the bra straps together in the back and they keep bra straps from sliding down shoulders, especially good for sloped shoulders. I use it on bras with permanent straps. They may not help if your bra straps are not adjustable, as when the back straps are pinched together,I have to let out the bra straps themselves. Hope this helps.

The picture shows the bra straps being pulled closer together than I want. Are these adjustable so you only pull them together enough to keep them up?

Yes, they are adjustable. You can even put two together if they aren't long enough. I keep them at the shortest length because that works best for me. I use them to keep my straps from falling off my shoulders. You do have to get used to putting them on yourself. Figure out what way is best for you, like twisting it around, hooking the bra, then hooking the strap.

How can you put them on if you cannot reach your back to hook them on??

I've never been able to close my bra by reaching to the back, I'm just not that flexible. So I close it in the front, then slip it around so the closure is in the back and thenI pull up the shoulder straps. Now, with the bra strap holder, I also hook that before slipping the closure around to the back. Before getting the bra strap holder, the right strap always slipped off my shoulder and I was always reaching under my clothing to pull it back up. No more! I really do like the strap holder.