I certainly don't doubt that India can build such a ship, and considering the rumblings over purchased ex-USN vessels recently I suspect that theres been a battle over whether to continue with it or buy another old ship. A battle won I hope in favour of the indiginous production of said.
USN catapults would seem the logical move, if they want this ship as soon as possible, which considering the time its taking, every delay must be ever more costly and worrysome for them. The technology is old on steam catapults, but the knowledge to actualy make them work well is now in centered in the USA and quite tricky so I've heard.
Russia experimented with them but had troubles so the rumour goes.
UK knowledge is contained in some very old documents relating to equipment no longer in use anywhere in the world.
Donkey boilers certainly have the advantage that their not dependant on the ships propulsion being active, nor do they drain that propulsion of power. But they do take up more space and burn more fuel.
EM catapults are not here now, and being new, there is all sorts of scope for delays and cost rises. Let the USN pay through the nose to develope this and proove it first.
As for slips to build a ship, I doubt there was ever a problem as such, but drydocks is another matter, they are the real limiter of ship size. Tonnage is not really a useful guide, its length, width, depth, and overall shape that matters in drydocks. As well as access and available workforce.
If I was the Indians right now, I'd certainly look at the PA.2 CVF variant for the next step up.
But then if I was advising the UK, I'd say have CVF built in India under such a deal, and the costs to all would be far lower.
Jumping straight to a Nimitz sized CV is quite a step operationaly and may not even be necessary.