"I am eligible for a free ASHP and solar panels" sounds implausible but I'll answer your questions anyway.
2. roof questions
Every proper 'MCS' accredited solar panel installer puts a few hundred pounds of your money towards getting a properly qualified surveyor or structural engineer to sign off whatever needs doing to your roof to put up the solar panels, hopefully just roof hooks to rails, but they are qualified to advise if yours needs more work first. It would be most economic to do your roof repairs first while the scaffold is up and then follow with solar panels. Do everything properly and you won't ever have problems.
1. running costs
I'll state what I did to get minimum running costs. That differs substantially from the big whole house plus water heat pumps which most people get done, and I've had it in place for more than ten years. I have a small air to air heat pump, like an air conditioner in reverse, as pictured. It is a simpler and smaller machine which never touches the existing hot water and radiators. The blower in the living room is pictured. It was intentionally sized to be frequently able to run at nil fuel costs well inside the photovoltaic capacity of 2.5kW(peak) which I have on the roof. Even in bright-cloudy weather, I'm getting most of the electricity free; enough to supply the 0.7kW(electrical) small heat pump to deliver 1 to 2 kW(thermal) of air heating.
3. I left in the gas combi boiler which is normally OFF. In the past 24 hours I used it for 2kWh of hot water in a few minutes and it has stayed off. To get this house to be comfortable when mostly unheated, I was careful with insulation and I don't have unnecessarily big exposed outside surface area leaking heat. In winter I'll use the old gas combi boiler central heating to radiators a little bit. The coldest day of the past five years used 30kWh of gas in 24 hours, and my gas bill last January was £1.50 per day.
If you really are in a position to get free stuff, do think through carefully what the motives are of the generous supplier. If they are building for plumbing and jointing practice then you might get an ideal home set up out of this. Try asking for someone to look at insulation, and lifestyle, which are my biggest two gainers for heating bill. If their usual thing is spivving up the quantity of electricity which you have to buy, then get the roof done, get the solar panels, insulate, and consider whether you could skip their generous offer of a heat pump. If their offer lists part numbers I'll read datasheets and comment.