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I could probably answer your question better if you had a specific problem or example, but they way I see it, unless they tell you otherwise through the problem or scenario, it is safe to assume that the pressure is constant (1atm) and that temperature is 25C, since that this the temperature and pressure that most biochemical reactions occur in.
You cannot really assume anything. It all depends in the problem and the information that they give you. As the person above said though, most reaction occur in the situations that they mentioned unless the question says otherwise. And besides the pressure being constant, it can say that the volume is constant and it would also make deltaH= q because delta H= delta U +PV so if volume is 0 then as I stated delta H=q. Thats another possible scenario.
Yeah I would also agree that assuming a constant pressure at standard state is reasonable if a problem does not specify anything. Two other indications that would point to constant pressure would be if the problem gives you ΔH to use because that is specified at a constant pressure. Another indication would be an open system, since that would most likely indicate constant atmospheric pressure.
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