Is a sandbox application feasible for an undergraduate thesis?
I'm thinking of creating a sandbox application in which a web surfer
could search any site he wants, dangerous or not. Everything that would
come from the internet would be trapped inside this application. It will
not be able to change anything outside the said app.

I have a few questions:
How technically feasible is this? Is it hard?
I've researched a bit about them and they say most of them wasn't performing
well what they were supposed to be doing.
I have no idea whatsoever in creating background applications. Everything
I have done are front side applications. Get input from user, process it, give
output to user.

Do I need to give special attention to things like client-side scripts, ActiveX objects, java apps, etc.?

Could read this:
Shows you how to set Firefox to low-integrity and run it without admin prompts.
Other browsers have their own protected modes, now.

And there's already add-ons like NoScript and Ad-Block Plus that block scripts and frames and other junk. So browsers are pretty secure now-a-days.

Otherwise you could write your own text based browser(unless you've got some GUI and graphic skills) and pretty much disallow everything.