A resolution advisory from TCAS indicates the vertical speed per minute that you must use to avoid conflict with the other traffic. Does this vertical speed given by the RA take into account the stall requirement for the aircraft?
Yes, but not directly. The TCAS is a generic box that doesn't really know anything about the aircraft performance. What it does have is a number of input discretes that allow other aircraft systems to indicate that the aircraft climb performance is limited. Other discretes code the altitude above which the aircraft cannot perform an RA climb. What drives these discretes will be unique to a specific aircraft type and defined during the STC process.
ARINC 735A TCAS Characteristic defines the following:
Climb Inhibit Discrete Input #1 through #4
Increased Climb Inhibit Discrete Input #1 through #4
Performance Limit Discrete Input
Aircraft Altitude Limit Program Pins
Based on these inputs the TCAS logic will compute an RA that does not require the aircraft to climb when it is not able to safely do so.
Aircraft performance should normally suffice to execute the TCAS RA in which case you are required to do so. If you can't fully comply with the RA, get as close to it as you can whilst protecting the stall envelope. This applies even if it means acting against your ATC clearance.
In case of any conflict between TCAS, ATC and stall warning, follow:
In that order of priority.