In a patient who has a very fast growing/high metabolic activity cancer, how small a tumor can be detected on a high-res pet scan?

1-2 centimeters. The sensitivity of pet scanning (in combination with ct) is dependent on the origin and metabolic activity of the cancer and the part of the body that is being scanned. In general, most 2 cm cancers will be identified; as many as 1/3 of all cancers less than 1cm may be missed.
8-9 mm. A radiologist might provide a more detailed answer, but i generally think of a cutoff of 8-9 mm, but that might also depend on cancer type, proliferator rate, and technical issues.
Depends. If the tumor is very FDG avid (takes up lots of the tracer), and is surrounded by tissue that takes up little/none, then it can be detected down to 5 mm or so. A more typical size is more like 8-10 mm, but remember, even that that is only 1/3 of an inch! an anatomic study, such as a ct, would rarely if ever call something that small suspicious except for lung nodules.