First time growing a lawn – questions

Hello, this is my first time trying to grow a lawn and I have some questions.

This is TTTF. I seeded about 5 weeks ago with some starter fertilizer. I water 3 times a day for about 8 minutes. This is in northern CA.

• I must not have seeded the lawn uniformly so it seems to be growing in patches. Should I add more seed to the empty areas, or will it grow and fill the space later?
• When should I add more fertilizer?
• Should I change my watering schedule?
• The lawn soil is a bit heavy and clay-like. I tilled the soil before seeding, but after several rounds of rain, it seems to have compacted back into a hard-like soil. Will this affect lawn growth? Is there anything I can do about it now?

Thank you.