She can legally operate as a sole trader without insurance as long as she works solo and has no employees but it is always a good idea for a cleaner to equip themselves with public liability insurance and any professional cleaner would have this cover, for your and their protection, solo or not.
She will be self employed so no probatory period is appropriate, when you are slef employed you are only there as long as the home owner is willing to buy your services, if you no longer want to have her you just cancel her services and she can do the same.
She may provide you with a contract or terms and conditions but a lot of solo operations don't have these in writing and all is discussed verbally.
Ask if she has a cancellation fee if you cancel a visit and if her insurance covers key holding insurance.
Ask her what is included within her service and what is extra and what is beyond the scope of what she offers. This is very important to find out in the first instance rather than be disappointed down the line if you wanted to book say a fridge clean for example and then find she doesn't offer this service. Make sure the service she is offering is right for you for both her and your long-term benefit you need to be a good match for one another or dissatisfaction will occur down the line. It's good if she has a service list in writing of all the items within the price she charges and what is additional to pay for. This clears up any potential misunderstandings over service level sold to you and you can see clearly what she has on offer within her service and whether this suits your needs.
For example, as a growing cleaning company, we have never offered ironing as an add-on, so if a potential client wanted ironing we let them know we are not a good match as this is not available and then they do not hire us to then become disappointed down the line. We also do not offer oven cleaning.
Some cleaners/services don't empty bins, some don't change beds, we do but others do not. it depends on what you want and what they are selling as to whether it will work or not.