Would the eldest son of the eldest son of a great grandson also be a Highess? That's what I've always gathered; problem is, I don't think the issue ever came up, but I figure there is an Imperial Household Law concerning the issue.
Don't Serene Prince/sses include all male-line non-morganatic descendants of a Russian Emperor that do not meet any of the qualifications to be a Grand Duke of Highness?
Dear Mat,
Regarding the title of Highness and the eldest son of a GD who was the grandson of an emperor. This eldest son is the representative of this cadet line of the Imperial House. Along with the style of Highness the representative of this cadet line also has a distinctive coat-of-arms. The arms, title and style descend by male line primogenitor
ad infinitum. I suppose in time this would have been changed had the monarchy survived.

The large coat-of arms of a Highness Prince of the Imperial Blood who is the senior male heir by primogenitor of a Grand Duke who was the grandson of an Emperor.
Regarding your second question, No. Certain relatives were granted the style of Highness even though they were not Grand Dukes. Some of the morganauts also hold the style of Serene. Of course there are the heads of the cadet lines that hold the style of Highness.
David