Translation:If she swims a lot, we support her.
Semantically, they mean the same but I think at this stage it is not allowed because they want to make sure we also learned the tenses correctly. Here in Dutch it is Present and it should be the same in English, especially since it's a correct English sentence and it makes sense.
No, it doesn't work. I don't think you would be misunderstood to say that, but that's not correctly phrased. I'm not sure exactly what the rule is here, but I think you only use "much" if you negate the verb or something like that e.g. "She doesn't swim much." is correct, but "She swims a lot." is how you phrase it without the negation. "She doesn't swim a lot." is also correct, but not "She swims much.".