The old chandelier only had two wires wired into the box and the new chandelier will wire into the same two wires. All the other wires are passing through and should not be messed with. Carefully inspect the two black wires from the new chandelier to see if they are exactly the same. Any difference, (ridges or stripes) means that it will likely be the white wire. Post the photos on here so that everyone can get a look at them.

You can not use staples to go perpendicular to the joists. Yes fix that. You can use boxes to extend things as long as they remain accessible. You can only staple things that follow the surface (along the joists or running boards). You don't need to use conduit (in most places) unless you're likely to have physical damage. You will need to secure things with an appropriate clip or whatever. Just dangling is not OK. Also if the basement is now considered unfinished, all the 120V 15A or 20A circuits need to be GFCI.

The simple answer is yes, you need need accessible junction boxes on both sides. However, if you still have the wall open where you want to frame the door you may have some other options. I am assuming the line you cut just connects one outlet to another in the wall. - For example, if the wire you cut is connected to a nearby outlet you may be able to rerun the wire and use that outlet as a junction on one side. - If you plan to add a light switch to either side of the door you may be able to use a higher capacity box and use that for box the wire junction on one side. - You could just add an outlet in the area to both sides of the door and use the new outlet boxes for the junctions. Bruce

Thanks. Yes, it turns out I was referring to BX. Thanks for clarifying. One portion of that circuit looked too "unfamiliar" to me so I ended up calling an electrician who took care of it. Just how crazy is this (1947 home owned by a DIY guy at one time): It was 10/2 sheathed cable from the panel going through a junction box with an outlet somehow spliced into it. The 10/2 then ran to a bootleg outlet in the ceiling and to that was the spliced BX (in a junction box). Anyway, I'm glad I called the electrician to straighten it out and get rid of the extra stuff.