old fuel and gasoline.

The HEF forum has some interesting stories .. and I'll wager there's a lot more that won't get told about fuel cross-contamination and mixups.
Just remember these factors. One - oil companies regard diesel older than 12 mths old as past its "use-by" date. It doesn't mean that it's unuseable .. it just means that it likely has become discoloured, lost many of its volatile ingredients that assist with easy starting .. possibly become contaminated with water (via condensation), microbial growth, rust, and general degradation of cetane rating.

Two - gasoline added to diesel reduces diesel lubricity - read increased injection pump wear. High grade kerosine is a far better additive to diesel.

Three - if you really need to burn that old diesel in your Cat, filter it thoroughly and dilute it with much new diesel. Buy new diesel and add a few gallons of the old diesel to every tank of new diesel.

Re the oils .. much has changed by way of oil chemistry and recommendations since the 1960's. Oils are much improved, particularly in the last 20 years or so. Cats recommendations have changed markedly in the last 30 years.

Use Cat powershift transmission oil in the transmission (TDTO) .. http://www.cat.com/parts/oils

These new oils are formulated for Cat powershift transmissions, and prolong their life. In the old days, the Series 3 oils wouldn't give you 2/3rds the transmission lifespan, that these new oils produce.

Final drive recommended oils are now gear oils - and the same applies as above. Yes, bottom of the fill opening is correct level. You are also well advised, to drain the finals, refill with diesel and run the tractor backwards and forwards for 30-50 yds in 3rd gear, to wash out all the metal particles.
Drain and refill with good quality gear oil of 80-90 wt. You should flush the finals every 1000 hrs, it greatly prolongs bearing life.

had written for the old mechanical systems that a small percentage of gasoline would reduce gelling and assist starting in cold winters.
I complained to a German guy and he told me they do it all the time over there in all the Diesels. (Good enough for me)
As far as old fuel in a storage tank that is filled full, condensation should be minimal and in a stable environment, not sitting in the sun but buried or in a basement so the temperature would be realatively stable.
I do AGREE that a good anti-microbial/water treament would be a good idea. In an old tractor, I would filter it and use it, though I would mix it 50/50 as long as its summer time. In winter I would drop back to 10 to 20%.