Is there any option to be out of the house while the work is going on? Rent a flat? Stay at a friends? Go on holiday? Park a caravan on your drive?
It would get you away from the dust and let the guys crack on with the work........
The wickes gate is probably the sort of thing that will fall apart in 5 yrs.
Go on, post a photo of your current gate.
You can make a basic picket style gate very cheaply and easily (if you have a few tools)
There might be a problem like a broken pipe, roots etc.
There are firms that will come out, clear the drain, and/or stick a camera down and do a cctv survey.
They key would be getting someone local who is reliable and trustworthy.
I know some people love them, but this is the disadvantage with cordless tools from lidl and aldi.
With the big brands like Milwaukee/Dewalt/Makita/Hikoki etc etc if at any point in the future you want more batteries/chargers/tools, you can just buy them with no drama
Wheeled mowers are faster over longer distances (straight runs), in a small area the turning slows you down.
I've never got on with hover mowers, would much rather use a strimmer, which would be faster than a wheeled mower in a small/odd shaped area.
You need a decent strimmer with a mulching blade for most of that.
Don't try and clear the lot (unless you're planning on building on it?), just make a way in so you can see what's there. Pull out any rubbish as you go, pile up the bricks/rubble.
You could pay a local...