Would there be a difference in meaning if it was just "do you guys have time?" without "the".

What does "up to" mean here?

"Up to" in this context means to be lesser than or equal to something else, but not greater. "Up to" here is better understood as a part of the phrase "catch up to". To "catch up to" someone means to reach the level or the distance of someone who has gotten ahead of you, but not to surpass them. Ex: I have one more person to catch up to in the race. Ex: She has the highest grade in the class, no one has caught up to her yet.

What does "joint" mean? Does it mean have a same with cooperating something? If so, can you show me some examples?

"Joint" in this scenario means "shared." The narrator explains that individuals in a scrum feel as though they have a shared responsibility for their work and successes. Ex: They have joint custody of their children. Ex: He and his wife have a joint bank account. Ex: The project was a joint effort.

When it comes to taking medicine, the preposition that's often used is "on?"

Yes, the expression is to "be on medication." Thus, when you are describing or referring to a specific medication/medication name, you can also use the expression to "be on X." Another similar expression is to "take [medicine name]." Ex: I take Tylenol for my headaches. Ex: I am on inhibitors for my high blood pressure.

What does “thrust” mean?

"Thrust" here refers to the force that moves an aircraft through the air. "Thrust" describes how powerful an engine is for an aircraft. Ex: The engine on this airplane has a lot of thrust.

When can I use "dude"?

You can use the word "dude" when speaking with friends or people you are close to. "Dude" is a slang English word for a man; a guy. However, this does not have to be gender-specific. Some women will call her female friends dudes. I recommend you only use this with people you are close to. If you use it with someone who is older than you, he or she might take offense. It isn't an offensive word, but it is not very formal with elderly people nor is it formal with people you don't know well. Ex: Dude, where is my car? Ex: Hey dude! What are you up to? Ex: Dude, this sucks! I didn't want to fail the class.