I restored some of my old Painkiller Black saves to see if I could level select. But I have found out that when I go to the singleplayer menu (Sign the Pact), it just restarts the whole game and doesn't give me the ability to select a certain level. Is there any way to fix this?

Go to load game and load the most recent autosave. That will take you to the chapter/mission select. Now you will be able to replay any levels you want.

What do you mean by: at the same time? Do you mean that the main levels and expansion levels are all in the "load game menu"? If so, then yes. I have went to the load game menu and saw the main levels and expansion levels availible for me to replay, as long as I had already completed them and had the autosaves there. Expansion levels or Battle out of Hell (BooH) levels will be there as long as they have been completed already.

If you mean having levels availible as long as the autosaves are there, then yes. For the expansion pack you will have to load the latest Battle out of Hell (BooH) autosave to replay any already completed expansion levels. These BooH autosaves should be in the same menu as the base game's autosaves.
I hope this answers your question.

Ok I see. So it looks like I just have to find the latest save in either the main game or expansion to load the levels. I was hoping there was some kind of level selector for everything, but I guess loading the saves manually will have to suffice.