Here are two words, "writing" and "riding". I know that there are two rules for them, as in the pictures. But in the first picture, can I say the /ai/ raising rule counterbleeds the tapping rule? I can also say the /ai/ raising rule feeds tapping rule, right?
Bleeding is where applying rule A first prevents B from applying, but B could apply if A had not applied – people often say that A "takes away" forms that B can apply to. Counterbleeding is where B would bleed A if B applied first, but A in fact applies first. By applying flapping first (which turns voiceless segments into voiced ones), you take away forms that could have undergone Raising (which applies before voiceless segments). Flapping applying before Raising is a bleeding order, because changing /t/ into [ɾ] removes an input to Raising. Applying the rules in the opposite order is counterbleeding. So, half right.
Feeding is where applying rule A creates a new environment for B to apply, and counterfeeding is where the opposite ordering would be feeding. No order of the rules affects applicability of flapping. The conditions for applying raising must be present in the underlying form: no rule creates a new environment for raising, so no order is feeding.
I agree with user6726's answer. I find that it relieves confusion to always state the counter-relations in the passive voice -- that way, the rules are stated in the order they would need to be in a linear ordering theory. If Tapping is before Raising, Tapping bleeds Raising. If Raising is before Tapping, Raising is counterbled by Tapping. (Likewise for "feeds" versus "is counterfed by".)
There is also an interpretation (also due to Kiparsky) according to which the difference in ordering is due to whether rules' environmental restrictions are relative to rules' input forms, or their output forms. For your example, in the counterbleeding dialect, the Raising rule is sensitive to its input, but in the bleeding dialect, it is instead sensitive to its output. In Kiparsky's terms, the bleeding relationship is "opaque", while counterbleeding is "transparent".