You should consult with your electrician and ask him if the following would be ok. I can only state it is what I would do.

The 14g solid is fine and is used where it will not be moving, bending, etc. Black is used for the Hot wire, White should be used for neutral. The screw terminals have two colors. Silver and copper or gold color. The white (neutral) attaches to the silver screw terminals, the black (hot) attaches to the gold color. I can see from your pictures you didn't do this, however, easy enough to correct.

Since you didn't mount the lamp sockets to electrical boxes, less than $1 each, you should cover all the expose electrical terminals with something, tape?, sheet rubber?, or build the box that you talked about.

I would not use that switch, as it is now, no matter how carful you think you can be. Instead, at the hardware store, buy a line switch, which then is part of the cord. Make sure the hot wire is wired to the correct terminal of the plug, which is also color coded in the brass or gold tint, neutral to the silver.

Might also be safer to plug into a GFI outlet if you have one.

Remember, better Safe than Sorry.