Term time worker - benefit implications

I have a (single parent) client who works 16 hours per week in term-time only, but has her pay spread over the whole year, so she gets around £534 every month. As I understand it, this means:

a) that she counts for WTC purposes as working 16 hours per week throughout the year, so qualifies for WTC, and isn’t subject to the benefit cap;
b) that if she were to move from tax credits to UC she would immediately become subject to the benefit cap, unless she were exempt from it on other grounds (which fortunately she is - see below);
c) that she is eligible for Carer’s Allowance (she has a child who gets PIP), because her earnings are below the CA maximum of £132 per week; and
d) that she would be eligible for SSP, because her average pay is (just) over the SSP minimum of £123 per week.

Have I got this right?

Yes, agreed. For completeness, it would also count as 16 hours for HB purposes (e.g. for the childcare disregard).

Thank you very much Charles.

I fear that, if she takes sick leave, the client will not qualify for SSP, because recent deductions from her wages (after she had to take time off to take her child to hospital) may bring her average earnings below £123 per week.

Unusually, however, she may still get contractual sick pay, as she is a local authority employee.

In this situation I am concerned that the client would lose her WTC four weeks after going off sick - unless she also claims new style ESA, which I understand you can get at the same time as contractual sick pay if you aren’t also getting SSP.