Lawns - seeding or turfing

Hello, I am a new gardener. Plan to work on the garden this spring. As you can see the garden has two parts separated by a stone low retaining wall, the smaller part has some grass growing on it but the quality is not very good, maybe just in winter time? the big part has nearly nothing because there were a few big trees just recently been removed. Could you please suggest:

1, I plan to hire a tiller to work on the left big part, I assume I don't need any weed-killer chemicals? In summer there are still some plants on but now there are not many because in winter time and recently removed trees and stumps, it looks bare.

2, how about the quality of the small part (right, around 60m2), grass growing on it but the quality is not good, is it a good idea to remove the turf or use chemicals and a tiller (which I think is easier)?

3, I plan to use grass seeds, much cheaper, this could be easier more than 200m2. Is this a good solution for the big and small parts of the lawns?

4, I live in Scotland, and the minimum temperature at night is still minus -2. is it good to tiller now and then wait until warmer to plant the grass seed?

5, the land is sloped i may also move some soil from the bottom/left to top/right to make it look slightly better /less slope. also may buy some soil, the quality of the soil may be not very good

6, also want to plant a landscape tree (not a very tall one), any suggestions on where should I do it and species? (the left is south)

7, is seeding equally good as turf finally?

Thanks