Potential Liver problem

Question 1: Does Apoquel work by being processed by the liver? i.e has vet ruled out this drug as being issue behind the abnormal bloods?
Question 2: could it be the bile duct being the issue rather than liver?
Question 3: There are a number of markers in the blood tests that relate to the liver, were any of these raised? (some are specific to the liver others are not)
Question 4: What tests is your vet saying are needed?

The first thing to say is the below is from my own experiences but you really should be having in depth discussions with your vet about your dog. You say your vet can not answer questions is that cos they dont have all the tests needed to do a full diagnosis? They should be able to talk generally if not specific and give you temporary guidelines of what you should be doing till you get a full diagnosis. If you are not happy with how your dog is being treated for this problem then discuss it with your vet and if needed seek a second opinion. 

My dog was very ill a few years back. She was sick, not eating and I just knew by how she was acting that she was really ill. It came on quite suddenly. All of her organs were enlarged but it was the liver that took the hit. It took me 6+ months to get her liver values back within normal range (one of her values was so high the vets own system could not read the value and so her bloods had to be sent to external lab). This year she has been diagnosed with pancreatitis and I can not help but think that this initial illness has caused her current issue just it has not become problematic till now.

The one thing working on your side if it is liver issue, as long as it is not too damaged, the liver is the only organ that has the ability to regenerate and mend.

There are different causes of liver issues so you vet my need the chance to ID why your dog has a liver issue (e.g illness, genetic..........).

If it is liver issues you may need to revise your dogs diet. Your vet or nutritionist linked to your vet should be able to advise on what you should be feeding.  

There are supplements such as SAME that can be given to support the liver.
It may be worth asking your vet about milk thistle as a supplement, my vet knew nothing about Milk Thistle so I have not used it but have a friend who uses it with one of her dogs that has a genetic liver issue.

For a short time my dog also had something to help bile production but can not remember the drugs name.

Good luck and hope your dog is on the mend soon.

Apoquel is an immunomodulatory drug that blocks the cycle of inflammation.

It is processed via the liver so should be out of the dog's system within 24 hrs (hence why it is administered daily) however it can cause elevated liver enzymes if given long term, especially at a high dose.  

Based on the blood results the drug should be withdrawn, if not already, bloods should be repeated and if neccessary treatment commenced. Unfortunately the liver can be quite badly damaged before any symptoms are present so this is not always a good indicator. Often once the drug is withdrawn the liver enzyme values will return to normal in time. 

Hope your dog is ok.