Yeah, the MS-I can handle most installations. The only thing that absolutely requires an MS-II is controlling a stepper motor IAC - they're distinguished by their four wire connectors. In some cases an MS-II is easier to wire up, though.
The Megasquirt uses a couple of external relays that are not included with the kit or an assembled unit, as they're not part of the ECU itself. These are there for supplying power to the ECU, controlling the fuel pump, etc. The relay board is a preassembled mounting point for the fuses, relays, and similar components, providing an easy way to wire up the Megasquirt for a car that does not already have the necessary relays and fuses. The relay board is designed so that you can mount it under the hood, and it connects to the Megasquirt with a single cable.