A lawn on a steep slope

Hello everyone

I'm new to forum so bear with me!

I've just moved into a house with a terraced/sloping rear garden - I like this as, from where ever I sit, I can see all the plants and so on.

My question here is about the lawn. The grass was cut for the first time this year about two weeks ago - it was almost a foot long! The level part towards the foreground is recovering well, with all this rain and mild weather. The slope however is a mess. It is my intention to add a few more railway sleepers to the left and right- you can see where I have been digging and make a couple more borders there. I then intend to shape the sloping lawn, rounding off the edges etc, but my questions are....

Slightly left of centre, you will see some longer grass. There are wooden steps here towards the seating area.

1) Is there a really good food/seed/anything to use at this time of year to help it?
2) Could I rake it at this time of year?
3) Where the wooden steps are, what's the best way to make it low maintenance? I'm thinking of sort of shaping in a path, but leaving the steps there. What about bark chippings?

I've just bought the house, so any help is really appreciated.

I'll start another thread about plant advice.

As I stand with my back to the house, looking towards the slope, I am looking due south.

The garden is about 47 feet wide.

Rusty