I've accepted redundancy but my about-to-be-former employer wants me to
work part-time under contract on a self-employed, sole-trader basis (ie
not as a ltd company)

1) They've offered me a rate of about double what my salary was - is
that about right to compensate for no holiday, sick pay, pension, NIC etc?

2) They don't mind if I work one day a week or one week a month. Is one
or the other better for NIC purposes?

Not sure HMRC would let me register as self-employed for one week a
month and deregister for 3 weeks to avoid 3 x Class 2 payments. I
already have enough NIC years for a full pension.
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Reentrant