New build, new lawn...

We have recently moved into a new build and paid the building company to install turf in our garden. When it was first laid, it looked pretty dead. Very dry, when you hit it you could see clouds of dust floating up into the air...



We complained, they told us this is just what new turf looks like after it's been transported and told us just to water it every day for a few weeks and it'll be fine. They also said that if it died they would replace it. We weren't convinced but decided to give it a try since they promised to replace it if we weren't successful.

Almost 4 weeks later and this is what the lawn is looking like..



There are patches where it has yellowed and hasn't really grown much, but they do seem to be getting better slowly but surely. Also patches where there is no grass and the soil is exposed but presume that's just from them doing back job laying the rolls of turf? We have not cut it yet but I understand I should be doing that soon, on a high setting, maybe next week?

I have also noticed that pretty much all over the lawn I have these little things growing amongst the grass, what are they? You can see them on the photo, it's all the little white dots. Is this just what grass looks like when it gets long?



Just wanted a view from experienced gardeners on how my lawns progressing as this is my first house and never really had much to do with the garden before. Thanks!