If the rebel base is hidden on a populous system loyal to the rebels. Can the rebel player deploy 2 units in the rebel base space and 2 in the populous system in the same turn?

Can the rebel player activate the system the rebel base is hidden in to move units into that system without putting them in the rebel base space?

Yes,

The rebel base is considered a completey different system to the system it is in until it is revealed. Exept for the purpose of moving units to and from the base.

"While the base is hidden, the Rebel player can deploy up to two units to the “Rebel Base” space. If the Rebel base’s system is loyal, he can also deploy units in that system. While the base is revealed, units cannot be deployed to the “Rebel Base” space."

Under "Deploy Units"