There are two important dates, the first is your review date and the second is the tier expiry date. If 31 December is your review date then you will remain as Silver until 28 Feb, however if your tier expiry is 31 December then the agent is correct and you will drop to Blue status but it is no "nonsense".
In any case, if you calculate a 13 month rolling period as at 31 January you can figure it if you will be able to renew your Silver status or not depending on how you flew the rest of the year.
Indeed.
The 'review date' (not sure if it is officially called this, but anyway) is at the end of the 12th month after qualifying for the tier. Then you still have 2 months of Silver benefits (lounge access at DXB, booking at business class counters and priority boarding). If you also get Silver bonus Skywards I don't know.