For your first question, what you're dealing with is "scheduled maintenance". This is down-time that large companies that have 24-7 service use for updates and other repairs to their service. Often, they won't tell anyone they're shutting down for a short while, and usually they will schedule this routine down-time for early morning on a weekend, when there are fewest people needing service.
Combined Telephone and Internet
I'm guessing here, but you're dealing with two different services, telephone and internet, on what looks like a single service: telephone service combined on-site with internet service. The same wires or fiber optics are leaving the building, but carrying two different signals on the single communication line.
Splitting of Signals
The two services may be leaving the building on a single communication line, but somewhere outside, the telephone service and the internet service are split apart. The signal dividing can be at the nearest neighborhood control box, or the splitting can be at the internet or telephone central office. I've even seen where the signals both go to the management company's corporate office in another State before the dual signal is split up.
I suspect that the phone lines leaving the building are not being routinely shut down for scheduled maintenance because the people you talk to at the phone company aren't being told of the scheduled maintenance. However, it sounds like the internet portion is being worked on regularly to clean up the virus protection and update other software during that maintenance period.
Your problem is that during this routine maintenance time, your fire alarm system will not call the fire department.
Your fire alarm technician will not be able to find the problem unless the fire alarm technician is there during this routine maintenance time. Then, the best the technician can do us to say "It's the phone or internet company".
Your GC electrician is not capable of changing the phone company's scheduled maintenance time. What the GC electrician is proposing, however, is a way of using a different type of phone service as a way of getting the fire alarm communications around your current phone company or management company.
I don't know how old the fire alarm system is in the building. There are also a number of other factors involved with whether or not the fire alarm system needs to be replaced, including what the fire department has to say. It could be that if the GC electrician is used to installing and servicing cellular systems, that may be a way to go.
With fire alarm systems, service after sale is almost more important than the type of system used. One way of figuring out if the GC electrical company is installing a reliable system is to make sure they will be the ones servicing the system for many years to come. If they just install a system, and then walk away after a year, they aren't standing behind what they install; if they install a system, and then service it on a continual basis, the are standing behind what they install.
Also, talk to property managers in the area who are using the proposed system, and talk to the maintenance people or caretakers. Both types of people have to deal with the fire alarm system in different ways. You need to be reassured from the management point of view and from the maintenance point of view that the proposed system is going to be a reliable system. (Reliable, in this case, means you won't be regularly called at random times because the system, including the central monitoring station communications, has intermittent troubles).