A player asked, as we are now doing some force powers.

Influence: The most basic form of Influence does not allow the Force user to guide or shape the thoughts of others. He can merely strain their mind, inflicting stress and exhaustion. The basic power has one effect that can be triggered multiple times on the same or different targets.

Does this mean that at minimum they MUST spend one force point AND inflict 1 strain at the base level of Influence.
If they then want to activate Control for the emotional state, they are now spending a second force point, correct? (2 total)

He wants to know if he can skip step 1 (strain) to go straight to step 2 (emotion)? If he can, is he still charged the force point?

The base power and the two control upgrades are different "power actions," as I call them. They are separate abilities that actually CAN'T be combined, they must be used separately.

So, yes . Your player can indeed perform a Mind Trick without spending a Force point to inflict a strain first. In fact, they cannot inflict strain while performing a Mind Trick (although I think it's a reasonable house-rule to say you can use both together).

The trick to determine what counts as a separate "power action" is to read the full description of the upgrade, and see if it says "As a action..." when describing what the upgrade does. If it does, then it's a different power action. Also, requiring a check when the base power doesn't is another good indicator.