Part 2 of the question has been dealt with in the previous answers, I'll respond to part 1 by providing a précis of this excellent article
Range and Replenishment
The VSTOL aircraft launched by ski-ramp mitigate the need for the higher into-wind speed of a nuclear carrier
Nuclear carriers require escort ships and tankers which are conventionally powered. The RN tankers will need to carry diesel in addition to aviation fuel so the range will be shorter but this is less of a problem for the RN since their fleet doesn't have to operate in the Pacific
Nuclear reactors require more manpower and are less flexible in their operations than gas turbine ships
Cats and steam
Nuclear propulsion has the advantage of providing plenty of steam for catapults. The catapult option for the RN ships would have used the alternative Electro-Magnetic Aircraft Launch System (EMALS)
Building capacity and capability
The UK would have had to provide additional land-based infrastructure to build nuclear carriers since Barrow, where the nuclear-powered submarines are built, is at full capacity.
The UK has never built a nuclear powered surface ship and would have to develop the expertise, and possibly a new type of reactor, from scratch. The French did this with the Charles de Gaulle carrier and had all the problems you'd expect with that sort of project
Nuclear engineers in short supply
The RN is already hard-pressed to find sufficient qualified personnel to man its existing fleet of 10 nuclear-powered submarines.
Attractive conventional options
Developments in electric motors and gas turbines have made the conventional option more attractive; more flexible location of engines, more internal volume, ease of access for servicing etc.
A nuclear carrier would need a mid-life reactor refit that could take the ship out of service for up to three years
The lifetime cost of a nuclear-powered carrier is much higher than that of a conventionally powered vessel. The initial construction cost is also greater because of the physical and regulatory complexity.
Disposal of nuclear vessels also presents a significant problem. the UK has yet to completely dispose of a single decommissioned nuclear submarine.
Nuclear vessels attract controversy and protest. Some nations will not allow a nuclear-powered or armed vessels within their territorial waters. Aircraft carriers are high profile ships and are intended as a tool for trade and diplomacy
Think of the paperwork…
British nuclear submarines and facilities are subject to strict regulation and inspection, including plans to mitigate any accidents that may occur. This would add manpower, cost and security overheads.