1. Are other planets flat too or is it just Earth? What about the Moon and the Sun?
Opinions differ, but most of us agree that planets are round.
2. Why do toilets flush the other way in the "southern" hemisphere?
You fell victim of an urban legend. There is no connection between a toilet's or sink's location and what way the direction in which the water will swirl. A quick Google search will bring up plenty of articles like this one to confirm this.
3. How thick is the flat Earth? Could we drill down and fall through it?
The Earth is at least 6400km thick, and drilling through it would cause you to reach its molten layer. Beyond that, it becomes somewhat meaningless.
(1) I have read that some FE's said that planets do not exist ?
How large are the planets ?
How far above the earth are they ?
(2) The toilet swirl question seems to be just due to the design of the toilet itself.About a bath tub, shower stall, sink, or lavatory , etc. drain ? Same thing- "just the design of the object" affects the direction of the swirl.
3)How has it been measured ?
What method ?
What's on the underside ?
What's beyond , or what's under , the underside ?
Is there a reference to these questions in the FAQ, wiki, ENAG , etc. ?
In the words of James Thurber, "You could look it up." ?
Here is another question.
Putting aside the question of hitting the molten core of the flst earth.
If you drilled that hole and you jumped into it , would the upward acceleration just come up and stop you ?
Just like jumping off that chair and the floor accelerating upward to meet your feet ?