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2. There is no "100% of IP from hitting infinity while offline."
There are 2 upgrades (that I know of) for that. One is the last Infinity upgrade, which is 50% of best IP/Min WITHOUT USING MAX ALL and the other is the last Break Infinity upgrade, which is 50% FROM LAST 10 INFINITIES.
As stated, and as you can see, they total to 100%, in optimal conditions.
It's always better to be online.
Online is better but because of actually progressing and modifying things, not because of those two bonuses.
Basically offline is slightly better than uncontrolled active run (when you setup the game and leave it for the same time as offline without touching it) but much worse than controlled active run (when you keep buying some stuff and adjust things from time to time).
My current Eternity length is slightly below 1 minute when online. With 200 eternity points/minute (133 EP per Eternity). There is a passive that gives 25% of EP gains when offline.
With default 1000 Amount in 4 hours I got just 2 eternities (1.5h long each) and 14k EP (58 EP/minute, so basically just gains from the passive). Calculations took just few seconds.
With 100000 Amount in 8 hours I got 170 eternities (2.8m each) and 50k EP (104 EP/minute, so almost 1/4 efficiency without counting the passive). Calculations took 2 minutes.