Toilet Pee Problems!

I don't know about the roof leak, as it doesn't explain the foul odor. I would be concerned about contamination. If you let water from other areas sit, i.e. from the kitchen faucet, does that also begin to smell bad?

I noticed that my toilet flushes poorly, that is, the rinse water flows in at top left, and circles the bowl, but does not do a good job rinsing down the back of the bowl. This quickly lead to an odor problem, although I did not notice yellow water on top of the flush flap. Perhaps that is what is happening to yours?

Anyway, our initial solution was a 1 liter soda bottle full of water left in the shower stall, and when you finished your business, you poured a quick rinse from the soda bottle at the back of the bowl as you flushed.

That was a bit of a pain, but a cheap fix. Then I discovered a $50 hand bidet at Lowes. It rather looks like a kitchen sink hand sprayer, but it taps into the water line to the toilet and has a handy screw holder thing that goes on the back of the shower wall, so it looks like it belongs there. Being right beside the toilet, it's a quick squirt in the bowl, and beautifully, it works great as a bidet, too. No more soda bottle, professional-looking installation, cheap, double-purpose, what's not to like?

Oh, it is also really handy for rinsing down the shower stall floor or walls. Much easier to use than the shower head.

To check for roof leak, close the toilet lid-put a bowl down on top of the lid. Is there yellow fluid collecting in the bowl?

I agree that it sounds like water is leaking from roof. My skylight was leaking and water in tub was yellow.. Until I happened to be in TT when it was raining hard, I didn't realize that was why the tub always was dirty and often had dirty water in it.

So it starts off clear and then turns a yellowish pee color within 30 minutes? That's weird. That sounds like either some foreign liquid or matter is getting in there and discoloring the water, or it's some kind of chemical reaction. Are you sure nothing could be slowly trickling in after it's flushed with clean water? Maybe a roof leak over the toilet? I remember we used to have a trailer with persistent roof leaks after hail damage, and the water in the floor would often be that color. It didn't have to be raining because the water was already up over the ceiling panels and would drip down through the ceiling lights whenever it felt like it.

It might just be the water supply (tank or city water depends what you used to flush is not clean).
Get the fresh water tank empty and clean,rinse/clean the water hose(check it separately),run water through your outside shower to see results.