You aren't comparing the price of nuclear vs. the price of solar but the price of nuclear vs. solar + hydrogen.

Oh crap, you're right. I got this confused with another discussion. Sorry about that. Anyway, the latter is a more meaningful thing to compare.

By your own numbers the price of solar is 3$ per watt while the price of nuclear is 7$ per watt.

That's cost per peak watt; a more relevant number is cost per average watt (assuming perfect energy storage at no cost). To get that, you have to multiply by the capacity factor. For new nuke plants, that's about 93%. For solar, it about maxes out at 20%. So construction cost per average watt would be about $7.50 for nuclear and $6 for solar.

Of course there's more to it. There's the cost of storage and backup, and maintenance, and of course the plant lifetimes differ by a factor of 3-4, and both types of power will get significantly cheaper to build over the next decade or so. But as a first approximation, you could do worse than multiplying peak cost by capacity factor.

While a nuclear plant can produce the same amount of power at night than at day it's not possible to change the amount that gets produced as fast as you can change how much hydrogen you burn in fuel cells.

Correct (for large light water reactors). Power grids do need the ability to adjust production to meet rapid changes in demand. What of it?