I have UK work permit, can I work in other Schengen Countries for temporary field work?

I'm afraid you can't. The United Kingdom is not a member of the Schengen agreement. You will have to apply for a work visa at the embassy of the country you plan to work in. I wanted to put the link in here, but that seems not to work (Y!A maintenance), sorry

As far as I know, a Schengen Visa is only for tourists staying max 3 months in the whole Schengen area (not in each country) so they might ask you when you come in from the UK after 3 months (or after 3 months to-ing and fro-ing) what you are doing. Don't say "I'm working," mainly because your job is in the UK not in the Schengen area, but also because, in my experience, the border officials won't know what to do because this is fairly unusual. The worst thing that can happen is that they stamp your passport that you can't come back for 3 months. I think you can apply for an extension of the visa, if you call your purpose for staying longer 'cultural study' 'language practice' or something, or even nominate a UK university where you are/might be studying if you can get your thesis idea about teenage dutch pedestrian behavior after drinking together but it's difficult and blah blah etc etc. In short, my experience is that border officials are rarely interested as long as you don't stay for a year or so on Schengen visa and then try to leave the country.

Its important to know citizen of which country you are. If you are not a citizen of the EU, then you will need a visa to travel to the Schenghen area. There is no connection whatsoever between your UK work permit and travelling to the Schenghen area, as the UK is not part of the Schenghen Agreement. If you, however, also have a Schenghen visa (plus the UK work permit) - then you can travel, as long as you are not employed and paid by an employer in the respective Schenghen country! To be sure, I would advise you to call/write to a Schengen state embassy (such as Germany, France, Italy, Sweden, etc.), asking them specifically, if a work permit will be needed for short-term field work, paid by your UK employer.

Unfortunately you cannot. If you were a Schengen Permanent resident you could work in any of the member countries for up to 90 days, but as the UK is not a member of Schengen. The UK is a member of the EU, but you would still need a UK passport to do this.

I would imagine that if you get offered the job, your new company will sort all that out for you. I guess if it's just short business trips, you might get away with using the Schengen, but long stays aren't permitted for work.