First of all, it is extremely rare for the yolk of an egg to become contaminated if the egg is reasonably fresh. Contamination only tends to occur when the egg is quite old and the yolk membrane weakens. (Source)
Now, that said, egg yolks begin to set at a temperature of 62° C (144° F), and salmonella can be killed at temperatures as low as 59° C (138° F), so it actually is possible to "cook" the yolk sufficiently to kill any bacteria without letting it set, but you have a very small window to work with, so you need to be careful. If the temperature is even 1° too low, you'll just be encouraging the spread of more bacteria, and if it's even 1° too high, you'll ruin your recipe because the yolk will set.
Nevertheless, if you have a reliable, uniform heat source, you could attempt to heat the egg to 60-61° C for about 1 minute.
Unfortunately, you won't be able to use the technique used in other recipes - such as Bavarian cream - of simply using the residual heat of the other wet ingredients to cook the yolk sufficiently for safety while not allowing sufficient time to set. Dark chocolate is the most heat-resistant but will easily burn at temperatures significantly above 50° C (125° F). Mixing the chocolate with cream may raise this temperature slightly, and I admit to not being certain of the exact amount, but I'm pretty sure it won't get you up to the required 59° C - and it really actually needs to be much higher than that because the temperature must stay that high for several seconds after adding the eggs.
So my advice to you is to either:
- Pre-cook the yolks very carefully to a temperature just below 62° C (use a thermometer!); or
- Use very fresh eggs from a reliable source; or
- Don't eat mousse made with egg yolks, if you can't tolerate the (very low) risk.
If the shell is undamaged, and the eggs are not past their expiration/best by date, they are safe to eat. Official source: your government's food safety agency, unless you live in a place with really really lax food regulation. But your profile says Australia - I'm sure things are fine there. If there are problems with salmonella outbreaks, it's not anything that you can detect. A salmonella-contaminated egg will look exactly like an uncontaminated one - that's why governments generally recommend you cook the egg, which will kill the salmonella and make it safe. If you're eating raw/undercooked eggs, you'll have to decide whether the risk where you are is low enough.
In practice, they're actually safe for a while after the best by date, just not as fresh, and if the shell is cracked without damaging the membrane or they were very recently cracked, they're also safe. But no damage and before the date is the most absolute guarantee you can get.
The two tests you mention will help you get some idea how fresh the eggs are. Neither has anything to do with good vs. rotten. As eggs get less fresh, they dry out a bit, forming a larger air pocket. So they'll slosh more, and start to float.
But it doesn't mean they're rotten. An actually rotten egg would be completely obvious by smell - they're sulfurous, a lot like the smell that's added to natural gas. If you're getting eggs that float in water on the day you buy them, with really obvious sloshing, yes, it means they're not fresh, so they're certainly not good as fresh eggs from a farm. So if that's the case, your supermarket isn't selling you good quality eggs. It doesn't mean they're unsafe, though.
As for "Why do most eggs have crap and blood on them?" ... "most" is a huge exaggeration, the places I've seen - they get washed. And as rumtscho pointed out in the comments, the eggs are coming out of a chicken, so some ugly stuff is natural. You never actually said what your eggs look like, but if you live in a place where they're not cleaned (even before selling in a supermarket??), then it still doesn't mean they're unsafe, just that you should probably clean them before cracking them.
And dark spots? Some eggs are naturally speckled - that'd be fine. If it's something else, I guess it would be helpful for you to provide a picture.
Best Answer
The FDA advises no more than 2 hours should pass between purchasing refrigerated raw eggs and putting them back into a refrigerator. 2 weeks exceeds that by 168-fold. Toss those eggs and purchase new ones.
There is no easy at-home test for salmonella, and certainly none as cheap as a carton of eggs. If you want to completely avoid the risk, I would recommend finding a source of pasteurized eggs. Barring that, get new eggs from the store and follow all FDA advice regarding their storage, handling, and cooking.