- whether or not the pass at todays old price makes sense for the very rough itinerary I have in mind for two people travelling within 21 days from NRT to Yokohama, commuting from Yokohama to Tokyo and back maybe 4-6 times, travelling from Yokohama to Hokkaido (Nizeko) and back to Tokyo, a couple more trips within Tokyo, and travelling from Tokyo back to NRT airport.
No. The only long trip is Yokohama to Niseko, everything else you can do cheaply on local trains/subways for which passes either aren't worth it or aren't valid.
As angra said above, flying is faster and probably easier. But if you do want to take the train you can get the JR East - South Hokkaido pass instead if that trip will be 6 days or less.
- ordinary or green
The JR East/South Hokkaido pass is only regular. If you did get green seats or a green JR pass, it comes with wider seats and more legroom (typically 2+2 instead of 2+3 or 1+2 instead of 2+2 depending on the train) but that's it.
- where to even order it and if there is a way to pick it up at NRT in case it is an actual card / pass, there might not be enough time to have it shipped
The JR East ones can be booked directly from the JR East website and picked up at major JR East stations including NRT airport (no shipping anything). For the full JR pass, timing and logistics might depend on the individual travel agent you book through, but I think the stations where you exchange the voucher for the pass are about the same as the JR East passes (but again, not recommended for your trip).
- is this JP rail pass all you need to travel within Tokyo on public transport or are there any busses, trains etc that are not covered?
Only JR and the Tokyo monorail are covered, all others are not. Many places in central Tokyo and the whole metro area will require other railway companies to get to. Short distance tickets aren't expensive but the Tokyo subway passes are pretty good value if you will be using the subway(s) a lot.