Paul,
1) For import into JomSocial, we still don't have a user-option to allow the import to happen. You can configure whether the profile is imported on registration or login, currently, but not by the user clicking something. We could help you implement this as we've helped others, and it still is on our to-do list, but it's simply not a highly requested feature.
2) The social profile plugins currently only import into text type fields. The reason is that the data from Facebook is usually 'free form' and could be any value. There's not really a guarantee that the country LinkedIn returns would be in the choices in JomSocial, or may be different, like "US" vs "USA" vs "United States". If you want to experiment, you can update the /plugins/socialprofiles/jomsocial/jomsocial.php file. In there, around line 55, you'll see:
protected function getProfileFields()
{
$query = 'SELECT * FROM #__community_fields WHERE type="text" OR type="textarea" OR type="date" OR type="birthdate" OR type="url" ORDER BY ordering';
Update that query to:
$query = 'SELECT * FROM #__community_fields WHERE type="text" OR type="textarea" OR type="date" OR type="birthdate" OR type="url" OR type="country" OR type="state" ORDER BY ordering';
That will allow you to see the state and country fields in the Profiles area of JLinked and map them to the state/country fields of Linked. From your other post about parsing out addresses, I think you probably can take it from here and translate US to United States or whatever is necessary.
We have hopes, later this year, to create the proper mappings for all the default JomSocial states/countries to what Facebook and LinkedIn return and have those as fields that can be imported into. It's just not something we support yet.
3) Unfortunately, I don't have any suggestions here. I've never really used their search, don't know how good or bad it is, and don't know of any replacements to suggest at all. Sorry I can't help you here.
I hope that helps, but if you have any other questions, just let us know.
Thanks,
Alex