I have a Mid 2010 MacBook. Is it possible to make the external display into the only one, so that I can close the lid and keep working on my MacBook with an external keyboard/mouse and monitor?
Yes. It usually "just works," but if you're having trouble, Apple has detailed instructions:
Yes, it is possible (I use mine like this al the time). All you need to do is ensure that the external power supply is plugged in.
If you intend on using this setup all the time, ensure you occasionally (say once a month), unplug the external power supply and use the battery.