Lawn spring maintenance: Order to do things?

My townhouse has a small lawn, about 5m x 5m. It's south-facing but one end is shaded, one corner particularly. This end is quite mossy and the corner has died entirely. I already relaid the corner with some new turf - the lawn is just starting to grow after the winter.

I have bought/got:

- Some 4-in-1 weedkiller/moss-killer/food/care dry mixture
- A tub of iron sulphate
- Some heat/cold/wet-resistant grass-seed, to over-seed
- A rake
- A lawn aerator

I'm not sure what order I should do things in. During the summer damp isn't a problem, only in the autumn, so I wonder if aerating for drainage is best done then - I want to retain water as the garden is a sun-trap in summer.
Is the 4-in-1 OK to use with iron sulphate, or does it replace it - we don't have lots of moss now I raked some out.

I haven't cut the lawn yet the first time. It's just starting to grow, but dandelions are already making an appearance and they grow like lightning.

Cut, rake, then spread the 4-in-1 and seed?

Be careful about overseeding after the weed and feed as the weedkiller in it will damage the new seed so follow the instructions on the bag regarding how long before you can over seed.

The 4 in one already has moss killer in it so save your iron sulphate.

Normally you would apply product, wait 3 weeks, scrarify to remove dead moss and then top dress and over seed. You could aerate at the same time as scarifying and top dress with a sandy soil mix to fill the holes

dont apply the product after the cut. apply midway between cuts.