As a verb, what does "sponsor [someone/something]" mean?

Why is present perfect tense used in this fragment (you've changed)? Can't I use just "you changed" instead? And when can I use the present perfect?

Present perfect is usually used to refer to an action or state that has occurred in the past and continues has an effect in the present. Ellen is stating her obligation to have the guests introduce themselves, as they "have changed" since the last time they were on her show. Simple past here would imply the action ended in the past and has no effect on the present. Ex. Her English has improved since she started using RedKiwi. Ex. She has been to Texas three times since last year.

What does "clumsy" mean?

If a person is "clumsy" it means that they are awkward in their movements and actions. They often have accidents and break things. It also means not being skilful in the way you do or say something. Ex: Oh no, I dropped a plate. How clumsy of me! Ex: Karen can be so clumsy. She bumped into George earlier and knocked him over. Ex: That was a very clumsy speech. The speaker was trying to be funny, but it wasn't funny.

I don't know how to use "shall" in the sentence, when can I use it?

"Shall" expresses the future tense in first-person form. It's similar to "will" and is sometimes interchangeable. It also indicates that something must happen. Sometimes, it is used as a polite request or suggestion. Ex: Shall we go? => polite ask Ex: We shall go to the party tonight. = We will go to the party tonight. Ex: You shall not leave this house. = must not Ex: If you're not here, I shall leave. = a conditional "must"

What does "blame it on" mean here?

If you "blame it on" a person or thing, it means you believe or say that they are responsible for or that they caused a situation or result. Here Monica is using it to say that Ross always says the reason she wins is something other than her skill. Ex: Don't blame it on your sister. This is your fault. Ex: I blame it on the weather.

Please explain the expression "into the production".

The term "production", as it is being used in this clip, same as the performance of entertainment. This can be a play, musical, opera or, as in this clip, a martial arts demonstration. Using "into (something)" is a very common way to express information about a part of a period of time. In this case, Conan is referring to the first 10 minutes of the entirety of this performance. So he is in (and has covered) those 10 minutes out of the total. Another way he could express this would be to say "after 10 minutes of the production". Ex: 20 minutes into the lecture and our professor still hadn't arrived. Ex: Only 1 hour into the journey I really needed to go to the bathroom.