Cities cooperation and services
Solution 1:
Do those vehicles are off duty in my town? Do they know when they are needed or I need to call them manually?
Vehicles assigned to other cities will migrate between your city and their city. They still spend most of their time in your city. You do not need to manually call them.
Does placing clinic, fire station near vulnerable areas make them safer?
Only in that the response vehicles can arrive on the scene faster.
Why citizens from city two don't want to do theirs shopping in city one?
Region management is handled on the server. Until you exit the game from a resource supplier city (saving it to server), the extra resources from that city will not be available to the region. Until you play a resource consumer city, that city won't see the extra resources available in the region.
So - play your shopping city and make sure there are unsold goods. Then exit the game, causing the shopping city to save to server. Then load the shopper city and wait for the local view of the region data to update (could take ~10 minutes). After that point, your shoppers should be migrating between cities.
If I have university in my region and no community college, will my other cities reach 3rd tech rank?
As of Update 4.0, students claim to migrate in the population details but do not. Tech points -do- migrate, and they lose their tech level-iness on migrating.
So - I had 1 city with a community college and no tech point consumers. It generates x tech points per day. I exit that city, reload the game and open a connected city. Those x tech points show up each day and promote the local industry to tech level 3 (only tech 2 should have been possible).
garbage tab, barely half is collected
The top number is the garbage collected by your trucks and should be used to make sure you have sufficient garbage processing to keep up (landfills and incinerators). The bottom number is the garbage generated daily. If there is no garbage in the garbage map, but there is a difference between these numbers, the most likely reason is that regional trucks have picked that garbage up. Regional trucks haul garbage out of the city, not to your dump - you do not need garbage processing to handle what those trucks pick up.
So - no garbage on the garbage map = all garbage collected, regardless of the x/y summary numbers. Your sims should be happy about that.