[Lizard]

1) Yes, you need OmniFocus 1.1 to sync across multiple computers.
2) Your OmniFocus data is stored in your home folder, not in the application itself, so you can replace 1.0.3 with 1.1. Or you can put one of them in a separate folder temporarily until you're sure 1.1 is behaving itself.
(I believe 1.1 is so much smaller because it is only in English at the moment. We'll add localizations closer to final release.)

3) Once you have OmniFocus 1.1, make sure System Preferences knows about your MobileMe account. Then open OmniFocus preferences and look at the Sync tab. (A big orange circle) There should be a Location field, which you can probably leave alone and a Sync Now button. Click that and your first sync should start.

The Help included with OmniFocus 1.1 has some more details.