I don't think minimum wage applies to the self employed, so paying less isn't illegal. Also the cleaner doesn't seem to do much and may be quite happy being paid less for light work.
I think that depends on the type of self-employment. Someone who charges by the job (eg a decorator) may or may not earn the NMW when averaged out. The rules are that it is illegal for an employer to classify workers as self employed in order to avoid paying them fairly, though.
I think there are often issues with what employers expect to get done in an hour, though. Things like cleaning fridges take me ages, as my knees are sore, but the cleaner is young and can whip everything out, wipe the cavity, wash the shelves and throw out any lurking vegetables in no time. A deep bathroom clean, OTOH is a big job, specially if she is cleaning grout. It's unreasonable to expect that as well as, say, cleaning an oven or other time consuming tasks. The best way is to talk through how much can be done in the time, and what the expectations are. Some rooms (eg spare bedrooms) probably don't need cleaning very often, but high traffic areas will need to be done every time.
OP, why not have a review chat, where both of you can say what you are happy with and what you would like to change/clarify? I did that after a few months, when I knew I was happy with her and wanted her to stay. We discussed holiday pay etc and what we both wanted from the arrangement, eg what happens if she has to leave early or cancel. I am usually in when she arrives, and we have a quick chat before she starts, so if there is anything I want doing I tell her then, and she can say what (if anything) will have to be left till next time.
In answer to your question, yes, I think the shower grout should be done and the kitchen floor should be properly cleaned in 2 hours, unless you are also expecting her to clean the cooker, change the beds and walk the dog😂. I would expect that, and at least a reasonably thorough dust and vacuum/mop in 2 hours. I would be 100% indifferent to a pointy loo roll though😉
If you like her, and feel happy with her in your house, it's better to have open conversations than any resentment on either side.