Are animal livers used in human transplants?

Not successfully. Animal organs have been used - in experimental circumstances - for a variety of human transplants, without long-term success. Remaining obstacles of rejection are major. When a winning strategy is developed, you will know because we will suddenly be able to address the organ shortage. We can use animal heart valves (usually pig) because they are treated + no longer stimulate an immune response.
Not usually. Animal transplants have been done, but this is not typical practice.The criteria for a donor liver include matching the blood type and also size of the donor liver with the recipient's needs.There are various other criteria also. A problem with animal transplants is that the immune system must be suppressed more than with human transplants in order to prevent rejection: more infection&cancer risk.