Plural of anything should never have an apostrophe, and since this context refers to a unit of measurement, rather than a name, I’d go with satoshis. Just like dollars or cents.

Similarly: “Bitcoin” the network (proper noun) or “bitcoins” the currency unit (regular noun)

Sats ⚡

Can I guess?

1 Satoshi is going to do something

2 Multiple items of Satoshi

Satoshi’s white paper

I have 1,000 Satoshis

Names are always capitalised, other uses are dependent and optional

If you are talking about people named Satoshi, I would capitalize. For a unit of bitcoin I would not capitalize. For both examples, I would use the second spelling for multiple.

I would use something like 'the Satoshi family' for plural just because I think it sounds better

The first example indicates Satoshi owns whatever follows