Choosing tense in a "that-clause"
Solution 1:
I believe that the 'is swimming' is correct and the 'will be swimming' is incorrect because in the second example sentence, the will would be repetitive.
It would also be incorrect logically because you cannot see that he will do something. You can only see him if he is currently doing something. So option 1 is correct. As to your second question, which is used after a that-clause, I would again say that is/ (in some cases, are) would be correct and not will. For example, the following two sentences:
- If you eat chicken in an hour, you will find that you are full.
- If you eat chicken in an hour, you will find that you will be full.
The first one is correct because you are full after you eat the chicken, and not at an indefinite point in the future, which is unspecified, and therefore incorrect.