It can fire up again. The lees is not 100% of the yeast in the mead. Depending on several factors it may fire up again."Is there any fermentable sugar left in the must, Is the ABV too high for your yeast, is there enough nutrients available?" moving it to secondary on top of new ingredients can affect any amount of varables to restart the yeasties. If you want to prevent it then you can cool or cold crash the mead & follow directions for using a campden tablet(s) and potassium sorbate to stabilize and prevent the mead from starting back up.
For your first question I am not sure of a completly correct answer. But mead takes months to age. If already in secondary then wait till completly clear and rack off any sediment. You have a choice to bulk age till it is at least 6-12 months old or bottle appropriately by using the method above to stabilize any possible restart of fermentation. There are probably other answers to your question so take mine with a grain of salt and keep reading.
A painting says a thousand words. But a painting while on good mead just looks funny!