Linate airport (LIN, Milan, Italy): can I go the night before for an early morning flight?

I have an itinerary that starts with a 6:30 AM Alitalia flight from Linate (LIN) Airport in July. Given this early start time and that I would be checking bags for an international itinerary so I need to be there early anyway, I am attempting to determine the feasibility of going to the airport at around midnight the night before. I have Skyteam Elite status (but not from Alitalia specifically) if that increases my options.

I simply cannot tell from internet search if Linate is a 24 hour airport. I assume it is, but if it is not, then this is not a feasible plan.

Internet search tells me that there are several lounges in Linate (both Skyteam and cash basis), which appear to open between 5:00 and 5:30 AM.

Alitalia's website (http://www.alitalia.com/en_en/informazioni-supporto/checkin/index.html) states to check in at minimum 45 minutes in advance for midhaul international flights (this leg is to CDG) but does not state a maximum allowed check-in window or time window that the check-in counter is open.

Questions:

• When is Alitalia in Linate airport open for checking bags?
• Is Linate airport in Milan a 24 hour airport?
• What facilities are available while waiting for an airline to staff the check-in desk?