2nd: You really don't every need to aerate. Never. If you feel like burying compost would be helpful (and I don't think it is), then you can go ahead. It shouldn't hurt anything but the time, work, and expense are worth considering. If you think you have hard soil you can fix that very easily by spraying the yard with shampoo at a rate of 3 ounces per 1,000 square feet and then following up with an inch of irrigation. Repeat that in 2 weeks and your soil should become normal again. Normal means the soil becomes soft when it is just watered and hard again in the days before you water. If you think putting compost in the soil will improve the organic matter, it might but just getting deep roots in the soil is the best organic matter you can find. Roots bring their own microbes which are the organic matter that really matters. Deep, infrequent watering is what the soil needs.

1st: Use the organic fertilizer at full dose of 20 pounds per 1,000 square feet. Look at the ingredients on the organic bag. If the first ingredient listed is feather meal, return the bag and get your money back. If it says it contains poultry or chicken litter, then you can use it, but there are better products. The feather meal is just worthless IMHO. A much better organic product is ordinary alfalfa pellets (rabbit chow). Search this forum for the pictures I've posted of alfalfa pellets in use. You can find alfalfa pellets at any feed store and most big box pet stores. You can find feed stores near you using Google Maps. Search "feed store san mateo".

3rd: Since you are in San Mateo you might be able to get away with using a chemical fertilizer this time of year but generally you don't use chemicals in the summer heat. Again, San Mateo is not typical of the rest of the world. The organic fertilizer (especially if you use alfalfa), is excellent this time of year. It will not burn at all like chemicals. With alfalfa, after you apply the pellets, you should moisten them (not saturate them). The next day they will swell up and look like green worms. You can drag a hose across the yard and the swollen pellets will crumble down into the turf onto the soil. Then they go to work. It will take a full three weeks to see the improvement - hence the term, 'slow release.'

@dchall_san_antonio- The organic fertilizer says 8lbs per 1000sq.ft. and the Gro Power plus says 25lbs per 1000sq.ft. Since I'm using both, do I do half 25 and half 8.