001. Does the order in which pax logging bundles are installed/started important?

No, you can install the two bundles, pax-logging-api / pax-logging-service, in any order.
However, it loggical order will be that frst you have the api and the the service.

002. Can I use Pax Logger in Eclipse (PDE)?

Yes. To have a smooth run just check outhe that you do not have the plugins related to looging selected in your run configuration (org.eclipse.equinox.log, org.apache.commons_logging, ...)