Can this laptop do these things?

Yes, except the 1080p part, because it won't actually be in 1920x1080 resolution since the laptop's max res is 1366 x 768 according to the specs.
 
Certainly it can do it! As correctly pointed out, the only thing that won't be happening exactly as you indicated is the 1080p videos on YouTube. You're still able to play them in a great resolution, but won't be 1080p.
 
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