This is tricky as the word recycle is normally used to reference waste management. It is also used like the word repeat. "The dull comedian recycles his material night after night." Maybe just say cycle 2 or the final cycle of the experiment?

The above are all good explanations. It's a silly phrase but common in America. Do not try to think of it literally. It can almost always be dropped entirely from a sentence and the sentence will make sense. "By the way, you should leave early for the airport because I heard there is bad traffic." You should leave early for the airport because I heard there is bad traffic. By the way can soften or make the rest of the sentence more friendly or it can be used in a negative way. It's all about the tone and way it's said. It will not often appear in email/news but will appear in literature.

Both are good. At the moment they are going to swim is more common than At the moment they are going for a swim.

The above is correct. You could say "this mistake might end up with me getting fired".