You are not liable under contract but you may be liable under tort or statute
You aren’t liable under contract because you don’t have a contract. However, neither do you have any limitation on liability a contract might provide.
The most likely and common-law universal avenue for liability is the tort of negligence.
Negligence requires three things:
- A duty owed by the defendant to plaintiff
- Failure to take reasonable care in discharging that duty
- Harm caused by that failure
The Scottish case of Donoghue v Stevenson (not English as it mistakenly says in the link), established that we each owe our duty to our “neighbours”. A neighbour is someone who should reasonably in our contemplation when we do the ting we do. These do not have to be specific people, they can be a class of unknown but foreseeable people. So, for all your examples, the person who eats the burger should be in the mind of the person who makes the burger, so a duty of care is owed.
Breaching the duty means failing to take reasonable precautions to prevent harm to the neighbour. What that means depends on the specifics of the case. For your examples, a professional chef is held to a higher standard in food hygiene that an amateur.
The duty doesn’t extend to eliminating all risk of harm but it does require that reasonable precautions are taken. Some of your examples seem to take no precautions regarding the time or the risk of contamination between the production and consumption of the burgers - this might be considered unreasonable.
The harm arising must be a consequence of the tortfeasors act or omission and must be reasonably foreseeable. Food poising is caused by contaminated food and is a reasonably foreseeable consequence of poor food management which some of your scenarios clearly are.
In some jurisdictions, there may be statute law that makes the supplier liable.
For example, in australia, the Australian Consumer Law imposes statutory guarantees on the supply of goods or services by a business even if they are gifts.
The most relevant being that goods must be of merchantable quality and fit for purpose. A hamburger that causes food poisoning is neither.