Retired on pension but starting as Sole trader question about N.I contributions

[asurfpro]

I dissolved my Ltd company recently after 10yrs in business and now plan to work on a self employed basis with a view to 15-20k gross per annum. I know I have to register as a Sole Trader and I am already registered
For self assessment.
I have a couple of questions if anyone can help me.

1. I am 69 and on government old age pension - shouldn’t that mean I don’t have to pay National insurance? Will HMRC just sort that out for me. I will be doing my own self assessments.
2. Does the requirement to register as Sole Trader happen after £1000 of business or net profit within the tax year?
   Thanks for any insight or thoughts on this.