When we wish somebody success, we do so in three general forms:
- ✔ I wish you success.
This form doesn't take any kind of article.
- ✔ I wish you a great deal of success.
This version uses the indefinite article, but success is preceded by an adjectival phrase.
- ✔ I wish you the success you deserve.
This time, we use the definite article, but an adjectival phrase is put after success. (A prepositional phrase is also possible in some constructions.)
In the versions in your question, you use the definite article, but don't follow success with a qualifying phrase. Because of this, the first version looks completely wrong, while the second version is unusual at the least.
The correction for the first sentence would be to just remove the definite article to match 1., while the second sentence would normally have in the world added to it, as in 3.
✘ I wish you the success.
→ ✔ I wish you success.
✘ I wish you all the success.
→ ✔ I wish you all the success in the world.
Note that as an oddity of how we've come to use English, the opposite is true of best. Unlike with success, I wish you the best is fine, as is I wish you all the best. On the other hand, again in contradiction to success, I wish you all the best in the world, while not wrong, is unusual. (And I can't think of any way of using the indefinite article with best.)
I can't explain why this use has come to be, all I can say is that it has.
The use of happiness is the same as that of success. You could replace all instances of success in the examples above with happiness and there would be no problem.