Advice sought on lawn care

Hello - love the site!

I have a 10x6 ft lawn which is very patchy. I live in Bulgaria - we have rain every day at the moment but very hot temperatures in between.

I have been overseeding and also transplanting 6inch high grass into the bare patches, but with mixed results. Am I wasting my time - should I just let the lawn repair itself? I don't have a mower (no space to store) so I use a trimmer, which leaves the grass quite high. SHould I just continue like this but not throw any more seed on?

Also, is it ok to throw the kids pee onto the lawn or should I dilute it a lot first? The soil is clay - when it rains, the garden floods quickly, but after a couple of days of sun it cracks up and is as hard as concrete.

Many thanks in advance for any help!