What is the shelf life of homemade peanut butter in winters and summers?
Per Pick your own (emphasis added):


  Store it in the refrigerator until you use it.  It should keep for a month or two. You can also freeze it.  It will keep indefinitely in the freezer. In both cases, you may need to stir the peanut butter to mix the oils back in (the oil tends to separate over time). And no, you cannot "can" the peanut butter - it is too low acid to safely can with home equipment.


I could not find a single government or university sponsored publication that discussed how to can homemade peanut butter.  If you stumble upon a certain link that does not eschew this practice, and recommends boiling temperature canning, consider them fraudulent.

According to Does it go bad:


  If you make your own peanut butter and you don’t use any stabilizers, you should keep it in the fridge. .... Your homemade peanut butter should be of best quality for at least half a year.


Note that all of the even semi-credible sources I could find indicate refrigeration is required.

At ambient temperature, especially in summer, it is going to have a much shorter shelf life, but I could not find any authoritative information.  You should probably prepare it in small batches that you can eat within a week, maybe two at the maximum  (in winter) if it will be stored without refrigeration. 

You also want to store the peanut butter so that the oil (which will probably separate) on top will protect the peanut solids, since it is more difficult for microfauna to gain a foothold in the oil.  Keep an air tight lid on it whenever you are not using the contents of the jar, to oxygen contact, and thus hold of rancidity. 

Homemade peanut butter will have mostly unsaturated fats (one reason the oil in your peanut butter is liquid at room premature), which are susceptible to rancidity.  You will want to discard the peanut butter if it develops rancid flavors as they are highly unpleasant.  If you see signs of mold or bubbles or sour or off smells, discard it immediately.

I suggest contacting your local universities, who may have programs or services to provide this type of information for your area and constraints (which I infer includes no refrigeration).

To the enumerated questions:


Sources seem to assume the basic peanut-only recipe.
There will be no significant difference for small amounts of additions of honey, sugar, or salt.  The amounts are too small.  Honey balances anti-bacterial effects, with adding moisture.  The amount of salt is just too small to matter.
See discussion above, there is no credible data that I could find for ambient temperature storage of homemade peanut butter.
See 3, only worse.  Those are incubation temperatures.  And how do you stand summers like that?