A picture would really help. I removed doors from closets and replaced with long curtains. I just used tension rods to hold them. I have discovered the 1/2 in conduit makes really nice sturdy rods and the heavier rod brackets hold them up nicely. And out from the wall just a bit to make your dispenser available to you again. Then you can make nice little cabinets out of the bi-fold doors. I made a china cabinet using 4 of them and Moccasin , here, made a nice bathroom cabinet for linens. both used the wooden bi-fold doors.

Yes, you can use half of a bi-fold door as a closet door. You say you have a finished closet opening; does that mean it is already trimmed out? If so, this article can help, and here is a video. These show how to turn a bi-fold door into a French-type door, but the basics of how they attach one of the doors applies to what you want to do. Make sure the door is not too tall for the opening and trim off anything that would drag on the floor. Since you will only be using one door you can add a stop (wood strip about 1" wide by 1/2" deep and the height of the door opening) on the side jamb opposite the hinges and attach the magnetic catch to it instead of overhead.

There are a couple of ways the wood panel can be set into the door. In the first, a rabbet is cut into the edge of the stiles and rails of the door. The panel is laid against the ledge formed by the rabbet and molding is nailed in place to hold the panel. Here is an ARTICLE showing how this is handled. In the second way the panel is set into a groove cut into the stiles and rales. Here is a PICTURE of how to put glass in place of a panel set in grooves. (The top half is the relevant part of the drawing.) Remove the panel by cutting out as much as possible. Chisel through the panel that is still in the groove in several places to break it apart . This panel should be floating, so once part of it is removed the rest should pull out easily.

We had louvered doors on all of our closets and switched them out. There was only one closet that we noticed a ventilation issues and we cut a hole and installed a vent. It's painted the same color as the wall and you can't even tell it's there.