I plan to tile a play area (290 sq. ft.) in my basement but I am not sure about some things. There is a drain field and sump pump under the basement floor. We have never had water on the floor except once when the sump pump failed and moisture oozed up through small cracks in the floor. That was years ago and we haven’t had a problem since. Here are my questions
• Can I put tiles down directly to the cement?
• If so, the cement floor is painted with oil base paint. I checked with rubbing alcohol and it didn’t come off. As long as I clean the floor with soap and water, is that enough or should I use TSP or something else?
• The shape of the space is like this; the A wall is straight for a distance of 33 ft. The B wall starts 5ft away from the A wall. After a 9 ft run it moves out to 9 ft away from A. After another 9 ft it moves out to 14 ft away from A, for the balance of the length. Where should I strike my line for the first course of tiles?
• One length of the tiled space does not butt up against a wall, it flows into my workshop which I am not going to tile. Do I need to secure something to the floor to make a hard edge for the tiles to butt up against?
• Is there anything I should do before deciding to go forward with this basement tile job?

I wouldn't attempt to put self stick tile on a basement floor. If you do, make sure you also use Armstrong vinyl tile adhesive in addition to the adhesive already on the tile. Not sure how any adhesive is going to react with a previously painted floor...

Have you thought about floating a vinyl floor instead such as Allure - sold at Home Depot. Moisture test the floor before you put anything down.

I would not recommend "sticking" anything to the floor and here's why:
Even a dry basement, such as yours, has some degree of moisture seeping through the concrete due to capillary action. It is after all a box of porous concrete, buried in moist and sometimes wet soil.

When you stick something like these vinyl tiles to the floor, assuming that they will actually stick, you will be trapping any eventual moisture underneath the tiles and giving the slab no way to breath and allow the water to evaporate.

Best case scenario: the tiles will come off.
Worst case scenario: the adhesive will hold but, depending on the components of the adhesive and the flooring, you might have to deal with a mold problem because of all that trapped moisture.

Then of course, there is the possibility that everything will work just fine for a long time but, as the vinyl gets worn, you might want to replace it, and the you will have to scrape all that stuff out, because installing another layer of flooring over the slab is a really bad idea.

I'd suggest you look into floating flooring solutions, specifically developed for basements like ThermalDry or similar. They are floating, interlocking pre-finished plastic tiles, 100% waterproof, 100% inorganic, mold resistant and built to keep the finished surface slightly raised from the concrete floor through a channel system that allows the moisture underneath to evaporate.

If your sump pump ever fails again, and your basement is under water, you can take the tiles off, dry them and put them back.
If a piece gets worn you can replace it without disturbing the remaining tiles, and if you ever get tired of them, take them off, donate or sell them to someone else because they will last for a long long time.