I have a few more doubts. Thank you.

1) I keep fit by doing exercise every day.
2) What are you playing at? (How would you rephrase it?)
3) He is making breakfast on his own/by himself/alone (Do they have the same meaning?)
4) Get moving ! I'm on my way. (How would you rephrase it??)
5) If they don't choose English, we won't be able to join the project.
6) Let's keep our fingers cross and hope that they choose English. (Can I include it in a email?)

1) I keep fit by doing exercise every day. Also ~~> I keep fit by exercising every day.

2) What are you playing at? (How would you rephrase it?)
It depends on what you mean by "playing."
What games are you playing?
OR
What are you trying to say?
OR
What are you tinkering around with?
OR
What are you doing?


3) He is making breakfast on his own/by himself/alone (Do they have the same meaning?)
Yes, they all have the same meaning.

4) Get moving ! I'm on my way. (How would you rephrase it??)
Start going! I'll be there soon.

5) If they don't choose English, we won't be able to join the project.
OK

6) Let's keep our fingers cross and hope that they choose English. (Can I include it in a email?)
Make it "crossed" and this is fine for an email, yes.

Of course, I'll be happy to help with your doubts!

1) To keep fit, I engage in daily exercise.
- Explanation: The sentence suggests that the individual maintains their physical fitness through the regular practice of physical activities.

2) What are you up to?
- Explanation: This rephrasing can be used to ask what someone is doing or planning. It carries the same idea as "What are you playing at?" but is a more commonly used expression.

3) He is making breakfast on his own/by himself/alone.
- Explanation: Yes, all three phrases have similar meanings in this context. They all convey the idea that he is preparing breakfast without any assistance from others.

4) Let's get going! I'm on my way.
- Explanation: This rephrasing encourages action and indicates that the person speaking is already on their way or about to start moving.

5) If they don't choose English, we won't be able to participate in the project.
- Explanation: The sentence suggests that if English is not selected as the chosen language, then the speaker and others won't have the opportunity to take part in the project.

6) Let's keep our fingers crossed and hope that they choose English.
- Explanation: Yes, you can include this phrase in an email. It's a common expression used to convey the idea of hoping for a positive outcome.