For the Photography CC package, does the $10/month cost go up after a year? Would I be committing for 12 months? Were I to cancel, could I use my perpetual license LR 5.7 or buy and use a perpetual-license LR 6+?
No, that is the regular/normal cost of that package. Adobe may raise it due to inflation etc, but it is not a promotional price that goes up after the first year.
The Photography bundle is a 12-month annual plan. If you canceled after the first month, you could change to another CC subscription plan with no cancellation fee.
However, standalone licenses are still available for LR6, and can be purchased anytime outside of CC...
Finally, in Lightroom you cannot move your catalog to an older version, like from LR6 to LR5. However, you can use the same catalog in the perpetual Lightroom 6 and the subscription Lightroom CC.
Hope that helps!