Is it normal to have a bad taste in the mouth after tonsillectomy?

Not usually. Sometimes the taste can be affected, hopefully short term, by the operation itself. In order to expose the tonsils a device is used which pushes the tongue down. If the operation takes a long time this device can sometimes cause temporary damage to te tongue. Rarely this can last a long time with change in the sense of taste.
Yes. It is common to have a bad taste in the mouth for several days to weeks following tonsil surgery. Occasionally, the taste buds on the tongue can get "stunned" by the device that is used to hold the mouth open during tonsil surgery. If this happens, it can take several weeks to months for that temporary change to recover.
Yes. This should get better with time. By 3-4 weeks postop, you should be feeling better.