No, it can't. The word "alternate" presumes another exists.
Not really. It depends on the interpretation.
In this particular situation it can be argued that Uhura said 'alternate' merely to confirm the fact that their futures are now different.
Therefore, it can easily still mean that the Trek prime universe (at least as far as canon is concerned) is no more.
What was also established by Spock is that whatever their future lives may have been, history was altered beginning with the destruction of Kelvin and culminating in the sequence of events they were experiencing then with Nero in the past.
Both Nero and old Spock can easily exist in the past even with the prime universe being completely changed ... passing through the singularity could have protected them both from changes in the time stream just as the Enterprise-E was protected from the changes in FC ... otherwise, the ship would have been obliterated from existence anyway (if the protection was only a temporary one from within the anomaly) since the Sphere was already attacking Montana before the Sovvie exited the time stream and inflicted casualties.
So to sum it up, there is a good possibility that the new sequence of events is actually happening within the prime universe we all knew.
In our reality, the previous Trek made shows and movies won't simply disappear ... but as far as on-screen is concerned, the prime-timeline from this movie's era and forth has been changed drastically.