If you take the start save, go into WB and generate a WB save. Choose "Play a Scenario" and you can play that map on different difficulties. With "Custom Scenario" you can change the options. Just note that barb tech are not adjusted for difficulty, so once you load the game you will need to add back barb techs per difficulty in WB. (see any NOble's Club game intro for how to do this)
Changing the Civ you play is a bit trickier but very doable. With the same WB save, open the file in Notepad. Scroll down until you see the code where Civs are listed and their attributes (there's 2 sections that need changing I believe near the top). Change all the civ/leader related code to the one you want. [One simple way to do this is to create a separate game with the civ/leader of choice. Create WB save and open that in Notepad too. Copy the corresponding code for that civ/leader over to the Wb save you want to play] Voila! new civ is in the game. You can do this to the opponents code as well.
One note: My assumption is you have the starting 4000BC save to generate the WB save. You can also do all this from a later save in the game. However, the process I describe will reset "buckets" like gold, research, great person points such that the game is not exactly what it was before. With start save there is no issue.