1) When are the imperial psalms to be chanted at Orthros? Is it EVERY orthros or just the Orthros on the weekdays of Lent? The HTM Horologion says every day. Other sources tell me it's for the weekdays of Lent? is there a difference between Slavic and Greek practice?
The Imperial Office, before Orthros starts, was a practice found in monasteries under the patronage of the Imperial Court. If Orthros is celebrated by itself, then it is proper to do the complete office. In many monastic settings the office is skipped entirely because it is not part of the Vigil. In a parish settings the troparion and litany are done, but the psalms are cut. Remember Orthros begins with "Glory to the Holy..." so everything before that properly belongs to the Imperial Office.
2) Are the psalms to be read or chanted? Our practice is to intone the hymns "O Lord, save Thy people" through "O Champion Dread" but never have we intoned those psalms if they are read before. And again, is there a difference between Slavic and Greek practice?
Properly done, the psalms are intoned at a pace that allows the Ecclesiarch to incense the entire church while the psalms are read. The rest of the office is then read plainly. What happens in parishes is the troparion are intoned at a pace to allow the priest the incense the church since the psalms are skipped. As for the difference between Slavic and Greek it comes back to the Vigil. In Slavic practice it is rare to serve Orthros when not part of the Vigil.