That is possible.

You have to click on this button, after that you can choose one of the selected Control Centers. BUT the Control Center must have other Centers set in the Settings

In general you can request all neighboring units in one call (though unrealistic). Availability depends on type of unit (not all are playable), shift time and probability (if you don't use 100 %).

Did you already check the tutorial in our Wiki? It's in German but should answer several questions when using a translator.

Sounds like you checked the wrong box in the options. In editor's "Einstellungen bearbeiten" you have your "Nachbarleitstellen" listed. You have two boxes right next to every neighboring CC. If the one under "W" is active, you will only see important (-> "wichtige") high level units such as ITWs and RTHs. This might be your issue - uncheck and NEFs, RTWs and FRs will be available. The second box active will also show KTWs (BLS). So if you wanna see all neighboring equipment only the right box has to be checked.

If this does not help consider giving us the ID of your CC so we can check for ourselves. Be aware of having it on public and not private mode.

These are points of interest. The tutorial will help you with this. Be aware that you also need all possible medical departments in hospitals somewhere near your CC (can also be in a neighboring) as well as gas stations to avoid routing towards Germany.

Those are tags for Care Homes specialized on people who are in need of a respirator 24/7.

Our admin explained it here as the Wiki cannot be updated due to a technical issue. Indeed kinda like KH.