My mother was an hcv patient who has acquired svr after therapy for the last 11 years. in the last 3 years she has psoriasis and she bleeds frequently. can she be infectious to a household member?

If SVR: Then there is no detectable virus in her blood which reduces chances of transmission greatly. You are advised to use standard contact precautions at all times.

Possibly: But unlikely. If she has sustained virologic response (?Svr?) there is nothing to transmit. If, however she still has virus in her system and bleeds onto an open wound in somebody else, that can transmit disease. This would be incredibly rare and virtually reportable.