You said a lot in a few paragraphs.

It doesn't matter what kind of grass you have, pee spots indicate an unhealthy underlying soil. You can improve the soil health by using organic fertilizer at least once a year. Since I went fully organic in 2002 I have not seen a pee spot, and I pee a lot ;-) with my two dogs (100 pounds of dogs).

Are your 25% weeds grassy weeds or broadleaf type weeds? If they are just broadleaf, then you could spray with Weed-b-gone and reseed a week later.

When you say it is lumpy, do you mean the soil surface is uneven or that the grass is growing in clumps? Fescue always grows in clumps, so that would be normal. You just need more fescue plants so the clumps blend together.

For the pachysandra bed, I would kill it, rent a power rake to rake it out (set the power rake to only get the surface stuff), grade/smooth, seed, and roll the seed down with a rented roller. You don't need straw (you said hay). I realize in some parts of the country, not covering new seed with straw is sacrilege, but it isn't needed. If you are going to do it anyway, be sure to ask for straw and not hay. Hay is animal feed and full of seeds from whatever plant it came from. You could end up with a yard full of alfalfa. After the seed is rolled down, start watering lightly, 3x per day, for at least 3 weeks. KBG begins to sprout in 3 weeks, so you have to keep after it.

You should not have a run off issue when seeding new grass. The light watering is meant to be very light to avoid run off.

What is your issue with the good side near the path? What is the path made of? Grass near concrete sidewalks and driveways typically more water because the concrete heats up and stays hot all night. That dries the soil out and the grass dies. All you need to do is water more deeply near the concrete. Sometimes you need to water more often - once deeply (normal) and once about 3 -7 days later to freshen it up right next to the concrete.