Can blood tests diagnose amyloidosis?

No. Amyloidosis is diagnosed by tissue biopsy such as a rectal biopsy wherein the amyloid in the tissue is detected by the congo red stain. It is the accumulation of particular misfolded proteins in the space between cells (extracellular matrix) that distinguishes amyloidosis. There are many types of amyloid proteins than can cause amyloidosis.
Sometimes. This can be difficult to diagnose. Sometimes it is necessary to take a biopsy, or piece of the affected tissue to examine it under the microscope to determine whether a patient has amyloidosis.