Well... You cannot create 100% unified fighter force between AF and Navy without serious compromises for Navy planes that are heavier (to sustain additional strength), have many AF unneeded parts (folded wings, massive undercarriage, arrestor hook force structure, etc) and so on.
MiG-29M/M2 and MiG-29K/KUB are the prominent try, but we will see its effectiveness later.
About nukes... All Russian fighters can carry them (except for export versions).
T-50 can carry guided (we'll see them later) and unguided nuclear bombs (including possible Kh-61P Grom-2 nuclear version) and Kh-59M2 light ALCMs that can carry conventional or nuclear warheads on demand.
I support a merger for a combination of lowering bureaucracy and increasing effectiveness. The navy has a stronger ability to project its forces over a wider distance, and unlike the army or airforce, it's already able to handle both armed men and aircraft.
I'm not saying that we should abolish the air force, but rather that the air force is managed as a subsidiary of the navy - essentially merging the air force into the navy's air wing. The land-based aircraft can still exist, but it's just that they'll be under the authority of the navy. i.e. the military revolves around the navy.
I guess it may make more sense for countries with a large about of coastline or a strong affinity with the navy, such as France, UK, Japan, South Korea, USA, etc... But India only really has one border with a real need for land-based military operations - and its aircraft can't fly into the Himalayas anyway.
India needs to make sure that it orders nuclear capable versions of the planes. I'm excited about the prospect of India ordering Shtorm with FGFAs.