What are the highest and lowest possible pH, paCO2 and HCO3 in the blood of living human?
As discussed in the comments, there are theoretical and practical problems with arriving at such data. There have been controlled experiments using canines, but you have specifically stated your interest in humans. I offer a summary of a few observational studies that may be helpful.

In this study, 117 patients in intensive care units (who are likely to have the most abnormal blood gas parameters among the living) were monitored with continuous optode-based blood gas analysis system. Of the 1,341 measurements, the ranges were:1,2  


pH: 7.14 to 7.64
PaCO2: 19 torr  - 98 torr
PaO2: 38 torr – 413 torr3


Another study included a total of 487 samples were obtained in ICU patients with severe respiratory failure and found the following ranges:  


pH 7.23 – 7.55
PaCO2: 19 torr – 83 torr
PaO2 30 torr – 522 torr3


These are reasonable ranges for pseudo-stable ICU patients. 
Contrast that with normal ranges (+/- 2 standard deviations):  


pH: 7.35 – 7.45
PaCO2: 35 torr – 45 torr


On the other hand, you’re interested in the most extreme recorded values, which are likely going to occur during cardiac arrest. According to this case report and literature review, the lowest published arterial pH of an adult who survived cardiac arrest with neurologic recovery is 6.33. The caveat here is that this was a near-drowning victim, and the associated hypothermia provides neurologic protection. The authors go on to report several others including their own patient with pH in the range of 6.5 - 6.6 with neurologic recovery in the absence of hypothermia.




Notes
  


1. Bicarbonate measurements on whole blood are calculated rather than measured and so not included in such studies. The more accurate test for this measurement is serum chemistry. The bounds are usually defined by the assay. It’s possible for a living human to have HCO3 less than assay (5 mmol/L in most labs by serum chemistry) or greater than assay (~50 mmol/L by most labs).
    


2. All data provided are arterial. Venous blood gases are of little clinical utility except as a cop-out for obtaining an arterial blood gas.
  


3. These upper values are intubated patients breathing 100% FiO2. (The lower values are those about to be intubated breathing 100% FiO2....) The theoretical maximum PaO2 on room air is derived from the alveolar gas equation, ~100 torr.