I'll try to hit'em in order.
P is expressed improperly on a fert label as P2O5.
P as an element (as far as plants are concerned)is actually half the amount shown on the label.
Drought. When you do have good soil moisture again, apply a 2-1-1 or 4-1-2 as directed to promote recovery.
If seeding, use a 1-2-1 or thereabouts. 18-24-12 as an example. Seed (& seedlings) has greater need for P than established turf.
Established. I mean older than 3 growing months. True, grass tolerates herbicides after 2-3 mowings. But "youthful hormones" run in turf for up to 1 year. During that time (& here comes some controversy), I feel that elevated Potash levels are in order.
Over doing any nutrient is wasteful & potentially dangerous to plants & the environment. Waste of money too.
P can cause a toxic condition when really over-done. Also, it can occupy available soil ions, displacing other nutrients or causing other deficiencies to occur.
Excess P is also beneficial to the developement of many common lawn weeds.
And surplus P can move laterally ACROSS soils & polute waterways.
K contains salts just like N. KCL (potassium chloride) makes a good de-icer & can harm any plant by reverse osmosis when over-done. KCL's salt index (or burn potential) is higher than urea.
K2So4 (Sulfate of Potash) has a much lower salt content & can thus be applied more heavily. But more than a plant can use is still a waste. I like to elevate K levels beyond conventional thinking when drought or other stress conditions are anticipated. Potash makes for stonger cell walls & better root density. The key here is to apply the extra K a few weeks BEFORE the stress period begins. Stress can also be traffic, insect, disease, or temperature related.
Agriculture grade ferts drive me crazy. The farmer doesn't care about fertilizer prill size when the stuff is being band applied right on the rootzone or row. In this case, it doesn't matter.
Size always matters on turf to some extent. Really small for greens (to avoid reel mower pickup & partical shatter). Mid sized prills around SGN 100-140 (-10+20 Tyler Mesh) for golf fairways. And a standard size (about SGN 240) is fine for higher cut turf like home lawns.
BUT, consistant sizing is very important when using agressive rotary spreaders. Big turf spreaders (over 12' swath) like PermaGreens, Lely's, Vicons, etc., are prone to striping when using AG grade fertilizers. The biggest prills travel furthest because they weigh more. (most of the ingredients have similar bulk densities) So if the biggest prills happen to be urea and the smallest prills happen to be potash then.....you get the picture.
I call this "ballistic particle segregation". I have no idea who coined this phrase, but it fits.
I could go on all day about this. But suffice to say, the only striped lawns I've had the pleasure to look at this year all involved improperly sized fertilizer ingredients. And all because ag ingredients are cheaper to buy. And some do work out OK. It depends on the range from smallest to largest. How small vs how big? You have to decide what works best for you.
When practical, absolutely do the soil test. You may decide to customize the program based on results (especially Lime). But you will also instill greater confidence with your customer when you present them with the lab results & a "custom program". This can make the difference between you selling a job and someone closing the deal instead.