The first sentence is said by Jimmy Fallon, the interviewer:
No problem, I've got you covered here. Here, this is for you. No problem.
At which point the show host produces a box and takes out two false moustaches.
The second extract is uttered by the Austrian-born actor Christoph Waltz:
I had this [he refers to the false moustache] erm... during a performance on stage in Vienna once um... A very intense scene where a girl, I think, tried to kill herself—in the scene—and, and, erm..um.. I was to convince her not to do it...
The actor has an excellent command of the English language, and his accent is clearer than many a native American speaker. His Austrian accent isn't as marked as Arnold Schwarzenegger's, but it is perceptible. The interviewer Jimmy Fallon is an American speaker. I have no idea where from in the States, I can only say for certain it's not a New Jersey or deep southern accent. Possibly he's from the East coast but I'm guessing; a quick search on Wikipedia will tell you exactly where.
Because it is an interview, and presumably the answers are not rehearsed, Cristoph Waltz mumbles a little while he searches for the correct expression or word to say next. This type of hesitation and mumbling is a typical and perfectly normal feature in everyday speech and one that can cause great difficulty for learners.