Hi Experts!

I have a very neglected lawn which has some patchy areas and is very lumpy.

Last year I started cultivating an area I wanted lawned next to the current lawn. I have done this but there is a difference in immediate height between the two lawns.

So I have 3 seperate problems which I'm hoping you can help me with.

Firstly the patchy areas - I beleive this could be down to lawn aeriation. I've never done this before and noticed there are 2 types of tools on th emarket. A 'barrow' type contraption which is a push along wheel with spikes in. The other is a gloriefied garden fork but it removes cylinders of turf for you to then brush sharp sand into. Which one would be more benificial and why do you have to use sharp sand? I have builders sand already so will this be of use?

Secondly, how can i remove the lumps from the lawn? I presume i would have to add something to fill in the dents but what?

Thirdly, (maybe similar to the above question) how should I blend the levels of the 2 lawns? grass type has been matched so thats not a worry.

I thank you in advance! Go easy with me, i'm relativly new to all this gardening business!