You can use confidence instead of lift.
For the second problem, you can (1) set a very small confidence threshold and a very large
number of rules (e.g. 1000), and then search for the rules you like; (2) construct a data set
only having income>50k and do the rule mining, where you will have 100% confidence and you can
use support to rank the rules; (3) balance the data sets, so that both income>50k and
income<=50 have similar number of instances, and perform the rule mining.
Any of the above three approaches is fine.
Can we choose whether we want to use confidence or lift? (all 4)