Can an advanced melanoma that has spread in all the body have signs in normal blood test?

Yes. Lactate dehydrogenase (ldh) can be elevated in metastatic melanoma. When it is, it is a poor prognostic sign. Another, less proven, test is called tumor antigen 90 (ta-90). It is thought by some to be elevated in advanced melanoma. I have found it to be nonspecific and no longer use it in my practice, however.
Yes. Yes it is possible. Unfortunately there are not reliable blood tests for metastatic melanoma, .
Possibly. It is possible. Usually, there might be anemia, abnormal liver test, or an increased ldh. Radiology tests and biopsies are more reliable than blood test in this disease.