1) Possibly trading my gaming computer for a netbook.
Not really a good trade.
2) Can a netbook run utorrent in the background and play a movie with VLC media player hooked up to an external source? Mostly my 19 inch widescreen...
Should be able to...
3) This is the netbook in question: acer aspire one d250
Yup, that is a netbook.
4) Also, how many tabs can you have open?
As many as you want.
5) Is there like a netbook emulator or simulator to test how they would run?
Try one at your local big box retailer.
As long as the CPU, chipset and ammount of RAM are the same, it will give you the same feeling.