How do you determine how much "life" an aircraft has left?
I'm going out a bit on a limb here, and it isn't specifically an answer to exactly what you are asking (which is what Stack Exchange tends to strive for), but I think this is the answer you need, so at the risk of receiving a couple of downvotes, here goes.


  engine was rebuilt 556 hours ago but was a problem because was never entered in the log books


I think that boldfaced text makes your entire question moot. In other words, the answer to your specific question doesn't really make any difference; the above tells you all you really need to know. Which is:

As Simon said in a comment, if the seller readily admits to not entering an engine rebuild into the log, then what else has not been entered into the log? Especially if you are a beginner, that's the sort of thing I would expect will come back to bite you hard.

Total time is stated as 6300, Hobbs time is stated as 7142, tach time is stated as 8131. And that's by the seller (including the mechanic's report provided by the seller). Does the difference between these figures inspire confidence in the airplane's state, the seller's honesty, and your ability to get an accurate picture of what you are buying?

As has been stated, the only person qualified to answer your question about the state of the engine in a reasonably objective manner is the mechanic who inspected the engine. The odds that this particular mechanic will stumble across this question is already quite low. What are the odds that the mechanic will not only stumble across the question, but also recognize the particular aircraft you are asking about and decide to answer the question with anything that is not already in the inspection report (which you already have received from the seller)?

More generally, with well-serviced aircraft, it isn't as easy as just saying "this aircraft has X number of hours of service left" even based on the current state of a single piece such as the (an) engine, because with good servicing it's perfectly possible to extend the service life of an aircraft for a very long time. A well-treated aircraft is a very different beast compared to perhaps a car (which might be lucky to get a checkup once a year and an oil change every few thousand miles), of course in part because the failure mode is much more serious. (If your car fails on the highway you pull over and call a tow truck; if an airplane fails in mid-flight then what do you do?)

Personally and for the specific situation you describe, I wouldn't go near that particular aircraft if I can avoid it, let alone buy it. At the very least buy something where the trivially obtainable numbers match.