ref: http://www.tokyometro.jp/e/index.html

Regarding the 1-day open ticket on a Tokyo subway...is it valid for unlimited use in the period of 24 hours from the time of first use or is it valid til midnight on the day of usage?

More of the latter, i.e. from the first train of the day (around 5.30 am) till the last (around midnight). Only valid on Tokyo Metro (formerly Eidan) lines. You pay extra to ride Toei lines. Combined ticket costs 1,000 yen - hardly worth it unless you take at least 6 rides.

You are looking at the Tokyo Metro web site so as Alec mentioned, unless you are sticking with the Tokyo Metro only, you either pay cash for the Toei line or get a combined ticket if you REALLy travel alot.

Tokyo Metro is the dominant of the two companies, but there are places only served by the Toei line.

We got a PASSNET prepaid card (the web site says SF Metro card, but you will get a puzzled look from people if you ask for that. The vending machine says PASSNET.) instead since we needed to use both lines over multiple days. The PASSNET vending machine accepts 10,000YEN bills, yeah.

if i wanted to do the loop on the yamanote line, maybe stopping at the most, 6 places, should i get the day pass? does the metro cover the yamanote line?

No. Yamanote line belongs to JR. There is a JR only day ticket that covers Central Tokyo (roughly within the loop line) for 730 yen (tokunai pass). Sadly public transportation isn't integrated and tickets aren't interchageable between operators.

alec; domo for the tokunai info. sounds like the right one for me. thinking about just spending a lazy day going around tokyo, getting off when and where i want, exploring, eating, and hopefully end up at a yatai somewhere at sunset.