To answer your questions though:
(1) I'd expect you to continue doing open source, as both part of the job and on your own. I do it, so should you. Case in point, we just integrated our site with WePay. WePay didn't have Java API, so I wrote one (along with my business partner) and we made it open source [a]. This benefited my company, open source and WePay all in one shot. This isn't the only one, I can point at many more large projects [b], [c], [d] (for just a short list) that we've either open sourced ourselves or contributed to. I have a clear history of coding in multiple languages. Anyone who is going to hire me knows my skill set without having to give me silly brain teasers or even read a resume. Why would anyone want to hire someone without a clear record like that?
(2) How you spend your time is up to you. There is a certain amount of work that needs to get done as part of the job and I'd expect that to get done. As long as you are getting your work done, in a reasonable time and of a good quality, I'm fine with whatever you do with your time. If that 'policy' doesn't leave you with enough energy, then I'd suggest either learning how to do better time management or find another profession / company.
As I already said, I wouldn't hire someone without seeing their source code. The single best way to really see it is to see how they've contributed and worked with open source projects. Bonus points if you find a unique project to create yourself.
[a] https://github.com/lookfirst/WePay-Java-SDK [b] http://objectify-appengine.googlecode.com [c] http://batchfb.googlecode.com [d] https://github.com/lookfirst/bootstrap
If your answer was "no", then my follow up question would be "so basically you wouldn't hire someone whose prior career had been spent at companies like yours?".
If your answer to the first question was "yes, option (2)", I'd have some follow up questions probing why the job is not able to provide enough interesting and challenging work to fully engage me.