Can XBAP applications access the TaskScheduler API? Are tasked created on the server or the client or both? Can TaskScheduler push data to an XBAP client?

It's all a question of permission level and if the callling process has enough authority on the computer. Regarding where you set the tasks depends on what you intend to implement but I'd say, out of the blue, the less applications you have running the better.
This might help get you started:
http://www.codeproject.com/KB/cs/tsnewlib.aspx

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Bigsby, Lisboa, Portugal - O que for, quando for, é que será o que é... http://bigsby.eu

Bigsby is correct, but I want to add thatby default all Xbaps, even fully-trusted ones, run without the Administrator's group token on their Process ACL. This has changed on Vista when running elevated for v4.0.

If you hit this issue, you can set the RunUnrestricted registry key for your Xbap, assuming it is also fully trusted.

Hope this helps,
Matt

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SDET : Deployment/Hosting