Answers, (though I only flew Aztec A, E & F).
If a tank is leaking, have it serviced. It could be a leaking bladder, which is a big job, or a leaking fitting, 'could be a small job. You should not have any concerns about how much fuel you take on because of a fear of leaks. If you have determined that it only leaks when full up, report that to maintenance, it will help with trouble shooting.
Yup, four up in an Aztec with a full few load on a hot day could get the oil temp over 200. That should be within limits, but if I'm seeing 225F, it's time to ease off on demands for performance in those conditions. I feel comfortable running 180F, and will tolerate 205F. 225F makes me nervous, other than for a very brief period, and I know why it's running hot, so I don't sustain it.
Seeing an EGT in celcius would be odd, but possible, I suppose. 1170F would be possible at a lower power if full rich. Lean the engines while watching for an increase, and you'll know what that instrument does. Or, better yet, while you're talking leaking fuel tanks with maintenance, ask them to identify and label that instrument, as well as confirming that it's working correctly.
An Aztec C is not a plane that people are probably pouring money into to upgrade, but that does not mean that you should accept a lower standard of airworthiness.
For your own sake, understand which engine has the hydraulic pump, so you'll know which engine failing means you need to pump the gear and flaps up. And, if you find yourself on a longer flight, cycle the gear up every half hour or so. If it takes a second for the gear lever to spring back to neutral, you know that the main gear had started to creep down a little. The Aztec F I used to fly would do that, and when everything was uniform quiet in the cockpit, you could actually hear the slipstream noise change as the main gear doors crept open an bit.