If your liver is inflamed for a prolonged amount of time, or if you have obstructions in your bile ducts is it hard on your heart, and might you feel pinching sensations or slight pressure around the heart area because of the liver issues?

Unlikely: Liver problems rarely if ever have a connection with your heart. So I would not be concerned about these vague sensations. The effects of bile ducts are largely felt by the liver which if the liver is diseased, it will cause abdominal symptoms.

No direct relation: liver problem can eventually create multiple system failure that could reach the heart, but having hepatitis, or and obstructive jaundice, then the person sickness will not affect the heard first ,but the dehydration and associated infection could make the heart speed up ,so follow with your doctor and follow their instruction.

Liver issues??: If you have serious liver issues you have a very serious problem. You or people you who know you will say to you that your skin has a yellowish tinge to it. The "whites" of your eyes will appear jaundiced (get it). You will feel itchy all over. You will be very sick, probably in need of a liver transplant unless it's due to Hep C and you have spare $89,000 which will cure it. Lucky you!

Not necessarily: if a vital body organ like liver is not working optimally, it would eventually affect other vital organs like heart and kidneys that sustain life. But there is no direct link between obstructed bile ducts with any schematic pain from heart. Feel better.