The USDA has this to say on it:
Storing Leftovers
One of the most common causes of foodborne illness is improper cooling of cooked foods. Because bacteria are everywhere, even after food is cooked to a safe internal temperature, they can be reintroduced to the food and then reproduce. For this reason leftovers must be put in shallow containers for quick cooling and refrigerated within 2 hours.
You'll find similar statements from government agencies around the world. The safe limit for raw or cooked food is 2 hours in the danger zone (40-140° F or 4.4-60° C).
If you're a restaurant owner or cook, you must follow this rule, hold hot foods above 60° C and quick-cool other foods before refrigerating. If you are not working in a professional capacity then you are not legally required to follow it, but if you are serving guests then it would be irresponsible (and possibly actionable, if someone gets sick) to do otherwise.
If you're an individual serving only yourself, then take whatever liberties and break whatever rules you want; it's your food, and your body. But there's no table or chart anyone can give you; there's no single specific point at which a food transitions from "not entirely safe" to "probably will kill you" because it depends entirely on the food, the environment, your immune system, and a plethora of other variables. The rule is 2 hours, period; any longer and there is some non-trivial risk to your health.
Some hints, tips, and warnings:
The 2-hour rule is a conservative estimate with a safety margin. Don't ask what that margin is. It's like asking what the "real" speed limit is on a posted road; you might know from experience, but it could change depending on circumstances and exceeding it by any amount means you take your chances and accept the risks.
Don't put large, hot items (such as an entire pot of soup or chili) directly into the fridge. The residual heat will warm up and potentially spoil other items in the refrigerator.
To quickly cool large cooked items, use an ice-water bath and/or divide them into small containers. (Note: Don't use an ice-water bath for cast iron.)
Don't assume that re-cooking an improperly-stored item will make it safe. Most bacteria produce protein toxins, which are actually the primary agents responsible for food poisoning, and several of these toxins are heat-resistant. Cooking will not kill or inactivate these toxins and eating the re-cooked food will still make you sick.
Don't assume that cooking "kills everything" and that a cooked food or cooking surface is absolutely sterile. Cooking kills enough to make the food safe to eat, but some organisms - such as bacterial spores from bacillus and clostridium - can survive the cooking process and immediately start producing more bacteria. Sous-vide bags, crock pots, etc. are not safe environments for cooked food in the temperature danger zone.
I don't think anything will be wrong with that milk.
- If it's fresh milk, which I doubt, you should consume it in less than three days.
- If it's pasteurized milk, which is much more likely, it'll be unaffected.
Signs of spoilage are a sour smell and sour taste. You should make a habit of always smelling your milk (food) before drinking (eating) it. If it doesn't smell like you'd expect, taste it. If it doesn't taste like you'd expect, ditch it.
Milk is cultivated with lactobacillus, a bacteria that's beneficial for us. So, even though milk may taste sour, it doesn't mean that it's undrinkable. In Holland, there's sour-milk (karnemelk), that some people consume (I don't like it, myself).
Under the right circumstances, milk will turn into yogurt, thanks to the lactobacillus...
At any rate, if in doubt, throw it out.
Best Answer
You can find out more than you'd ever want to know about cooking eggs safely in the International Egg Pasteurization Manual. The standard USDA guidelines for pasteurization of plain whole eggs require 3.5 minutes minimum holding time at 140F (60C).
(Note: Holding temp here refers to egg temperature itself in liquid form: see edit for clarification below. These times/temps are NOT sous vide water bath temperatures for eggs in shells.)
As you can read in that document (particularly Table 6 on page 12 and Table 29 on page 25), adding in small amounts of salt or sugar increases the requirement for pasteurization by various amounts, up to 6 degrees F (3.3 degrees C). Yolks or whites alone also have different numbers.
So, it's really hard to generalize here. Particularly if you start to include any dish that may contain eggs, the required pasteurization temperature may vary a lot. If you mix in eggs with a good growth medium and then slow-cook that mixture for a couple hours before it hits ~130F, there will be a lot more bacteria to kill than in an intact whole egg, hence requiring a longer or higher temperature process to make sure the food is safe. And different textures of food, different moisture levels, etc. will also affect pasteurization. Yes, in general if you hold eggs long enough above 130F, you should eventually kill off enough bacteria to make the food safe to eat. But there's no easy formula for it, particularly if you include mixing other things with the eggs.
If you want to be safe, the easiest thing is often to buy pasteurized eggs or follow the 60C/140F recommendation for 3.5 minutes with whole eggs to pasteurize them whole yourself. Then you can mix or combine them with other foods with less worry. The only major egg property impaired by pasteurization at 140F is the foaming of egg whites. (Egg white alone can be pasteurized at 136F (57.7C) for 6.3 minutes, which will retain much of the foaming properties. With whole eggs, going above 140F, even by a degree or two, begins to inhibit other baking properties; see the linked document for details.)
EDIT: After a comment pointed out some ambiguity here, let me note that the linked document is only about liquid egg mixtures. That is, if you break your whole eggs and bring that mixture to 140F, they will be pasteurized in 3.5 minutes. If you are cooking eggs in shells in a water bath, that's going to be a lot more unpredictable. Larger eggs will take longer to come to temperature, eggs that start colder will take longer to come to temperature, and water baths that have a very active circulator will heat eggs a lot more quickly than a static water bath. If you want to ensure safety for eggs cooked in shells, you'll have to hold quite a bit longer to ensure they reach adequate internal temp, but that time is unpredictable because of the above factors. There are sous vide guides out there, as noted in the question, that give much longer times to try to ensure safety for eggs in shells. Sous vide guides can't give minimum temp/time with as much precision as the pasteurization guide in the link here, because most people aren't monitoring the internal temp of their food in a water bath.
I was originally trying to address the question about cooking eggs in general (not just "boiled eggs in shell") and dishes containing them safely, which would mostly involve liquid eggs and various mixtures including them. And the only way to be precise about minimum time/temp is to specify final internal holding temp, as you'd measure a turkey or whatever. Minimum overall cook times will always be estimates.