No one is disappearing. Q hotels have at least adequate WiFi. Of course, having a phone with an international data plan is a good backup.
The time can and will vary. Right now, a few cities are experimenting with shortening the quarantine period. If some new variant pops up with a longer incubation period, then quarantine might be extended everywhere. In general, you can get a fairly good idea at how long Q will be by checking the absolute latest regulations for your arrival city a few days before getting on the plane. To be safe, the best bet is to count on all time of "home quarantine" or "community health monitoring" to really be more time in a Q hotel.
Yes, if you turn positive, you will be isolated (still with WiFi) until the local health department is sure you are cured. Since different people recover at different rates, there's no firm answer on how long a positive person will be spending in an isolation ward or Q hotel.