FYI, Jobroller is a wordpress theme and not plugin.
Anyway, no option on this yet with the theme and will require code customization to implement. The theme is not encrypted and so it can definitely be modified according to your requirements. Implementation is just dependent upon your coding skills or you can just hire a coder to do it for you. Appthemes also have some certified community partners
http://www.appthemes.com/partners/ that can be contacted for customization jobs.
The job submit form includes next and previous (Go back) page navigation.
2)multiple page form with next and previous page navigation
Same with number 1.
3)can this form be save while not ready for example if the user is at page 4 out of 8 pages form and they want to save and continue later (povided they are logged in of course)
Users can edit their submitted jobs on the account dashboard.
4) will users be able to edit their own submitted form?
Jobroller has a search feature with radius parameter capability, if this is what you mean.
5)are there any search fields
You may check the demo page here
http://demos.appthemes.com/?theme=jobroller to try out some theme features first.