Running a 1hp (or even 1.5/2hp) motor on 120v shouldn't be an issue at all. Two belts sounds correct. 3+ HP generally has three belts for most saws. Is there enough of the motor plate there that you can identify the actual motor? You might be able to obtain visuals online to make up for the missing information. Some folks here will also likely know what connections to check to see if the machine is setup for 120v or 240v now. There's no real benefit to running on 240v so your desire to be able to use the saw "anywhere" via 120v (and appropriate amperage) can be achieved.
Relative to dust collection, the poor performance isn't really about a missing motor cover. It's more about these early machines had no way to have the airflow come from the blade or even the middle ground of having a sloping floor to the DC port. Current generation modern saws even have a shroud around the blade inside the cabinet.
--
The most expensive tool is the one you buy "cheaply" and often...