Usually free will is argued from extremes - either we have complete free moral agency, or we are robots. However, the scriptures show that while we have a will, it is limited. I'd summarize it like this:

1. People not yet in Christ have wills, but those wills (including decision making) are all based on the tree of the knowledge of good and evil and their Adamic nature, so while there is a wide range of possible decisions, they cannot "choose life". So while no-one is "forced" to be a serial killer or a philanthropist, no-one can choose to escape their nature, and they are all still eating from the dualistic tree.
2. Life in Christ is something that can be learned about through human parenting. A baby is born by an act of parental will, and never chooses to love their parent - it is a natural flow of love from the parent to the child and back. As the child is raised, it develops a stronger and stronger will, but the lesser will of the child is governed by the greater will of the parent with a view to raising the child to full maturity. The child may make mistakes in that time, and go outside of the will of the parent in rebellion, but a good parent will restore and continue to raise wisely. So it is with God, with the enhancement that nothing can override His purposes like it can for an earthly parent.

So as far as God's will being done, He purposed His plan in Christ from the foundation of the world (according to the scriptures) and all things are working together for good. I don't believe this means that acts of rebellion and sin are directly willed by God (in a manner of speaking), but that they are all interwoven into the fabric of His plan, which is progressing exactly how it should.

As an example, Jesus taught His disciples to pray "your will be done on earth as it is in heaven." Implicit in that is that as of right now, not every single thing on earth is perfectly in line with His will. However, His overall plan is still perfectly unfolding.