1 - Yes. "The target also takes persistent bleed damage equal to your precise strike finisher damage." Finishers don't mention that you add the precise strike damage to the base Strike by default, because it's covered by the base precise strike feature (and because, in theory, you can use finishers with attacks that don't qualify for precise strike, although bleeding finisher and confident finisher specify that you must).
2 - Yes. This is less obvious, but was clarified in the FAQs/errata relatively recently. Open the CRB errata (3rd printing) section and ctrl+f for "bleed."
Thank for clarifying. It almost seems too good to be true, but then again my character is spending a lot of actions in order to gain panache where a different class (fighter/barbarian) could just stand and whack multiple times getting out consistent damage instead of incidental peaks.