Problems with new Turf.

Hi, I posted late last year after re-turfing. Grass died? in loads of patches yellowing despite staying wet. I'd raked in a modest amount of fertiliser prior to laying the turf. I'd mowed too low (and too early apparently). Advice was to leave it until the growing season started before re-acting.

As it's close to the time, I've tested the soil and got a 7 on the ph and negligible or nil readings on nitrates, potassium and potash. I was intending to spike the lawn and apply a mix of sandy compost and seed. It obviously needs a heavy feed as well. 

Any suggestions for the best way and sequence to resolve this? I guess applying feed and seed together would be wrong? Is a ph of 7 also a bit high?

Very grateful for advice.