How to partially upgrade a site? I'd like to redevelop a site on my  local machine (which takes a few days to accomplish) and then import to it only the nodes which are created on the production site during this period, so that importing new nodes does not undo changes made on the local version and then I can migrate the redeveloped version to production without loosing recent activities. 

I am wondering whether it is possible, and how? I appreciate your hints.
Depending on the complexity of your nodes (if using custom fields or references) you might be able to use the node export module to export the nodes as CSV files and on the new upgraded site use Feeds to import them. Keep in mind that if the nodes NID are needed for an specific menu the NID might not match.

Note: you might also want to check the migrate module as well as the deploy module.