She has said that it is a legal requirement that I have this certificate in order to work with food but I'm pretty sure that's not quite right!
Food hygiene rules & the certification requirements vary depending on area, type of establishment, and your actual position; however I doubt the truth in her statement which seems to be implying anyone & working with food has to hold one.
Knowing what kind of establishment you are talking about and what your position is would help gauge how relevant you're holding a current one would be.
(I work in catering, for a large company which through a number of arms supplies food to thousands of people, it is standard practice for anyone starting a new job in the company that their PVG (broadly equivalent to CRB) comes through before they get to start work. This is paid for by the employer.
Everyone directly involved in catering (through this company) receives training & sits an exam which leads to REHIS certification. I assume this would be the equivalent to the expired one you mention. This is carried out usually within the first year of employment, and again is paid for by the employer.
If your employer wishes you to have this certification, the onus is usually on them to provide or fund the training. They should also pay for any examination &/or certification fee. Any time you spend at training for this should either be during your work hours and paid as normal OR paid as overtime if it out with your normal or rotated hours.
Before confronting them with your concerns with regards this part of your contract, I'd suggest clarifying the regulations as they are relevant to your area (both geographically & area of employment) Your local Environmental Health website should be able to point you in the right direction. Once you find out what the legal requirements are, you are in a better position to request amendments prior to signing.
As for your zero hours contract which should be fucking illegal by now, why the hell aren't they?!, if it was never mentioned that this was how you were to be contracted; I imagine you have a pretty good case to request a minimum hours contract. They won't necessarily agree; but again, if you can find out the legality of them giving you this type of contract after not advertising it as such (I think you said this?!) you may have some leverage.
I'm sorry I'm not able to give any specific yes or no answers, but as I said, the regulations DO vary so I'd need more info.
I do hope you get it sorted out satisfactorily!
And as others have mentioned, if they aren't going to play ball; sign the contract only if it doesn't mean there are any penalties for you and start looking for something else.
Don't pay for the certification. If they deem it necessary, it is up to them to pay for it.
The only time you should be asked to pay for training etc is if there is a clause in your contract stating that if you leave within a certain period of time you are liable to repay for any training costs that have been incurred.
(E.g. HGV licence training costs £thousands, you would probably have a clause dissauding you from immediately move to a rival firm as soon as your employer put you through it)