Check with your local fire department.
Go the park, a children's museum, any educational facility around.
Politely explain that they are not keeping up with the arrangements you both agreed upon and that even though you would love to be a replacement for mommy and daddy you aren't.
Yes I believe it does count as experience as you would treat the children you're watching as one of your own.
Someone fun, adventurous, creative.
I would just simply let them know well in advance so other arrangements can be made during my absence.
Income needs to be reported to the IRS/Social Security so when you are eligible to receive Social Security benefits there is a record of your wages. Being paid under the table creates no work history therefore no Social Security benefits.
I'm never sick enough to miss work.