Alfa Romeo Mito - various issues and MOT advisories

Does this mean the ESP has failed or is this just a side-effect of the dead battery?

Could be a side-effect of the dead battery - especially if the problem doesn't re-present when you restart the car.

Something called a the "Poly-V" belt has snapped? What would this be and what is it used for?

The Poly-V belt most likely drives various ancillary components off the engine - not sure what on the Mito to be honest but could be things like A/C compressor, alternator etc. Potentially even the power steering pump - which might explain the issues you were having with the steering (although I wouldn't expect it to get lighter if the belt snapped!). Usually a poly-v belt snapping isn't a major job to do and it's unlikely to have done significant damage to anything.

There is also damage to the sills after I drove over a small island and impacted them - can these be replaced or renewed?

Depends on what the damage is - if we're talking cosmetic damage to sills then this is something you can do things about. If it's more significant, structural damage (which is unlikely unless you were going at a significant speed) then it's a problem - sills can't easily be "replaced" as they make up part of the main chassis of the car. Essentially you need to cut our the affected sections and weld in replacements.

Like I say though this is unlikely - it's most likely just cosmetic damage. If there's sufficient damage to expose the bare metal beneath any paintwork though you'll want to address that sooner rather than later. The last thing you want is the sills rusting on you!

Last year's MOT came with an advisory for front brakes being imbalanced and that the system either needed readjusting or repairing (3.7.B.5B) - there is a grinding/scratching noise when braking, could this be related?

This is probably your most urgent problem to address - if the balance was so far out that it barely passed that's not good. You're going to need a trusted garage to take the front brakes apart and have a look - it could be something as simple as just needing new discs and pads or it could be a sticking piston on one of the calipers. Brakes are an essential safety component and a substantial imbalance in the fronts could see the car's direction pulling significantly to one side under heavy braking - and depending on what side that is could see the car slewing into either on-coming traffic or some poor sod on the pavement.

Another advisory states "OS Front Suspension corroded but not seriously weakened" what does this one mean?

It means basically what it says - the OS ("off-side" a.k.a. driver's side) front suspension has begun to corrode but that so far it's still doing the job sufficiently. Assuming this was on the previous MOT then it may have progressed since then - if it's corroded too much then it will need to be replaced.

Given there's a reasonable length list of various issues and you mention the car has been stood for a year I think the wisest course of action at this point is to take the car to a trusted garage/mechanic and have them assess what the car needs doing to be made roadworthy and go from there. Several of the things you mention relate directly to safety-critical stuff (suspension, steering, brakes) so they aren't things to ignore or take chances on.