Does the NES classic run at the same speed as the original NES? If I were to get a really good time on the NES classic, would it not actually be said time?

I have been looking for a ROM of this game but most of the ones i can find either get cancelled by my anti-virus or are slowed down or sped up so can someone please provide a usable ROM?

So I am new to the whole speedrunning thing and I was planning on a Super Mario Bros. run but I don't have a NES USB controller but I DO have just some random controller I got for my birthday so is using a NES controller required or can I use said random controller?