Growing a Lawn

What’s the best way to get a lovely green lawn? We have tried seeding and feeding but just get loads of dandelions everywhere. 

Can I sow new lawn seed just after treating lawn for grass grub? If not, how long should I wait?

I have recently had a new ready-lawn laid by a qualified supplier. It’s now sprouting dandelions and tiny fungi (mini ‘mushrooms’). The ground was prepared properly and I did have dandelions in the old lawn but no fungi. I am digging out the dandelions and ensuring no flowers mature. I am also pulling out the fungi daily before they spore, root included, but they are still appearing in even greater numbers. Any solutions?

Instead of having a ‘regular’ lawn, I would like to plant native grasses and tussocks. What would you recommend? 

I’m trying to update my front yard by growing a bit of grass. What is the best way to sow grass seeds? Also, when is the best time to do it and do I need any special top soil?