Brainstorming is a process for stimulating creative problem-solving. It includes coming up with as many ideas as possible, but not stopping to evaluate them until later. It requires a facilitator, to keep the group on track, but I am not sure if this is the same thing as "the driving force."

More often than not, strategic planning holds out only one scenario that underplays the unpredictability of the world: and so, providing (from the outset) the participants of a brainstorming exercise with a list of driving forces is likely to reinforce blind spots. In scenario analysis, the usual process is to uncover the focal issue, make out key factors, and only then list driving forces; the subsequent process is to rank the driving forces, flesh out scenarios, draw implications, and select indicators.

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Not actually. Brainstorming is a communication technique which is often used in faster problem solving/decision making.

You may find useful information here: https://www.mindtools.com/brainstm.html

To answer your question, you need to understand the group you are working with - their level of maturity, their blind spots, their purpose for doing scenario planning, etc. in order to determine the best way to go about approaching the work. There are many ways to do scenario planning and to meet the needs of the group you're working with. What is most important is that there is collective clarity and agreement on what the driving forces are as well as a fact base that supports their reasoning. Otherwise their discussion is little more than an opinion fest and will likely begin to show cracks when decisions need to be made.

The objective of brain storming is to check whether the initiators of the session have missed any blind spots. So if you give the driving forces up front it could have two outcomes - stereo type answers which the team already knew, or something new which the team had missed earlier.

This is where the moderator's expertise comes into play - to constantly track the progress and if the session is heading in a direction which we already knew, the Moderator needs to play the devil's advocate to divert the discussions into unknown terrains.

But personally I would not give the driving forces earlier. Let the participants come up with a list of driving forces and the scenarios for different combination of these forces. That way the ideas generated will be large in numbers.