thickening lawn ans relaying lawn

[hisumesh]

Hi All

I am looking for guidance on 2 things related to my lawn.

1) As can be seen from the image, my lawn is thickness/green patches are uneven. What should I do to  fix this? How often should I do it? How long will it take for the results to show up?

2) There is a section of lawn which despite all efforts (and thanks to all the advice and guidance from here) I’ve not been able to regenerate. I’m thinking for re-laying it as a DIY project . Any guidance on how I should go about? My lawn is buffalo. Attached is the section I’m referring in to.

Thanks in advance