edit: I see now you can upgrade the command ship to process crystals by right clicking and choosing upgrade from the dialog.

edit2: also, it appears you have to do in-place upgrades on frigates as well. Docking them is not sufficient for an upgrade.

In Mission 8 I recon'd the crystals and researched the tech. The workers refused to harvest the crystals. So I built a processor and then i was able to harvest the crystals. Is that normal? do you have to have a processor? I noticed the command ship shows a 'crystal processing' ability in yellow but the processor shows the ability in green.

It's been a while, but iirc an ability in green means that unit has the ability and can use it immediately.
If it's in yellow it means the unit has the capability to have that ability but needs to be upgraded in order to use it.

I think upgrades can also be started by selecting a unit (or units) and pressing <U>.
If a unit needs to dock to upgrade, pressing <U> should automatically set them to do that.

Command ship should be able to process crystals on its own, so long as it's upgraded.
Processors and carriers can also have the ability.