Hi Josh,
Welcome to Cantera! Although I haven't used Chemkin since it was purchased by ANSYS, I'll do my best to answer your questions.
1) Cantera cannot generate mechanisms itself, but neither can Chemkin. Cantera (and Chemkin) provide the facilities to interpret mechanisms and solve the equations representing the variation of the properties of several relevant systems.
2) Cantera does not have any built-in mechanism reduction facilities. You will have to implement an algorithm yourself, or use one of the algorithms generated by our community (e.g.,
pyMARS)
3) Unfortunately, I don't have a recent copy of Chemkin to be able to compare. If you do, I think we would all be interested in seeing the comparison.
General thoughts on Cantera vs. Chemkin Pro: Cantera is open-source software, which means that you can see the algorithms that are used to solve problems, and potentially improve them. In addition, if you find bugs, you can fix them. Neither of these are true with Chemkin Pro. Cantera also has models for several non-ideal-gas equations of state, which you can use in the zero-dimensional reactors. Last I checked, this was not possible in Chemkin, but again, its been a few years.
As far as I can see, the only advantage of Chemkin Pro is that it integrates by default with ANSYS Fluent, if you want to lock yourself into the ANSYS ecosystem. Perhaps one other advantage is that Chemkin Pro (used to) come with a full GUI for all the capabilities, if you feel that you require a GUI. To me, this is a disadvantage, because Chemkin didn't (doesn't?) come with the ability to script interacting with the program, so it is hard to use it to do large analyses and very hard to customize. Up to you whether this is an advantage or not.
Best,
Bryan