They are not directly connected but it's extremely likely that an ECB increase will also lead to an increase in varibale rate.
Yes cost of funding is related to other factors. Mainly the cost that Irish Banks and Government are paying to borrow, the later being currently at 5.8%
However all Irish banks are loss making, due to high cost of funding and bad debts due to poor lending practices. The losses need to be turned around so they will up rates at every opportunity.