This took me several hours. I did have other things to do today, but ah well, this was much more fun. Thanks for the wonderful puzzles. :)
And the three puzzles:
*** Detailed Solution ***
With just Nurikabe logic, we can get this far:
Now it's time to switch to the Slitherlink:
Switching back to the Nurikabe,
And this gives us more information for the Slitherlink:
And now we have enough to finish off both halves of the puzzle:
You can get this far with relatively simple arguments based on a single clue at a time:
Then, there's a useful pattern to notice:
That deduction can actually be extended:
And now it's time for a big deduction:
And now we can finish off the puzzle, with just single-vertex deductions. The solution is below:
With one teensy correction to the final slitherlink (EDIT: Now corrected!), @kristinalustig has already solved this puzzle. However, I thought it would be beneficial to provide something a little more step-by-step to supplement her excellent answer, so that anybody following along and getting stuck would have a resource to guide them through...
This was fun! Here’s how I solved it:
You can get to here pretty straightforwardly:
From here, bottom left must be green and the top can also be filled in:
The rightmost must be blue, making two below it green. From there the colours need to alternate, with the bottom being red. We get the solution:
Here is the solution with the "true" slitherlink clues and happy stars representing shaded cells in the nonogram puzzle.
To start the puzzle observe that
After that, the rest of the solve is relatively straightforward.