When do you hear the Ping sound of the lid sealing

This is the cheapest chamber vacuum sealer that I've come across: VacMaster VP112. At $669, it's half the price of most other chamber sealers. Chamber models are far more "professional" than the stuff marketed to the home, and my understanding is that they are far more reliable.

The difference between a chamber model and a home model is that you place your food in a bag in a chamber. The entire chamber is used to create a vacuum, meaning that liquid won't leave the bag. A home sealer will also not go below atmospheric pressure while a chamber unit can get a much higher vacuum allowing for vacuum marination, compression or fruits, and better flavor penetration during sous vide, which may or may not hold any interest for you.

In terms of your specific questions:

1. My understanding is that these consistently make a good seal.
2. I can't speak to longevity, but these are the kind of units that restaurants use for sous vide prep, so I assume they take a beating in those environments.
3. Because it's in a vacuum chamber, liquid is no problem, and you can actually vacuum seal just liquid.
4. Major Fail. These things are big and heavy. The one I mentioned is 24" x 16" x 9" and weighs 53 lbs.
5. Shouldn't fail to seal. Not sure about waste if it does.
6. Cannot be used with a container, but why would you need to rather than using a bag?
7. Minor Fail. The model I listed is a little over your price range. Most other models of this type will be between $1,250 and $7,000.

The other consideration is chamber size. You obviously can't vacuum pack anything that's larger than the vacuum chamber. The one is listed has a chamber size of 12" x 11" x 5".

Yes, fast chilling is critical because it minimizes the production of new bacteria and potentially deadly toxins from the spores of anaerobic pathogens such as C. botulinum and C. perfringens. The spores are not killed by the low temperatures usual in sous vide, and the oxygen-free environment of the bag brings them back to activity. But they require time and temperature to become active and dangerous, so fast chilling -- either refrigeration or freezing -- and limiting the refrigeration time (to about 5 days at around 5°C/40°F, longer for lower temperatures) are absolutely critical to deter them.

The question starts with a situation that is different: cooking in an oven, which is not an anaerobic environment and thus does not trigger the same activation of the spores' lifecycles as cooking in a vacuum does.