Also, I am unfortunately far from well informed about Elizabeth. Was she ever legitimized by Peter?
She was, and he openly acknowledged her, raising her in his court as his daughter. However, the fact that she was illegitimate at the time of her birth was used by her enemies and was one of the impediments to France's accepting her as the wife of Louis XV, which Peter had proposed.
Elizabeth's reign, bracketed by the reigns of Peter "the Great" and Catherine "the Great", has always received relatively little attention. However, recent scholarship has begun to recognize it as far more substantive than popular wisdom holds. In its own way, her ability to stay afloat during the potentially-hazardous reign of Empress Anne and her bloodless coup to supplant Ivan VI and cut off his mother's aspirations to remove Peter's lineage permanently from the line of succession was as impressive as Catherine II's more-famous coup twenty years later.
In some ways, Elizabeth was the last of Russia's larger-than-life monarchs who lived and ruled with a wild abandon that, paradoxically, endeared them to Russians. The vast scales and the exuberant decorative excesses of the Winter Palace and the Catherine Palace were her creations. (In fact, Catherine II later painted over much of the exterior gilding of the Catherine Palace, finding it too expensive to keep in pristine condition. And, although noted for her architectural interests, Catherine II's construction projects never approached the scales of what Elizabeth erected.)
While contemporaries probably would not have seen it this way, the passing of the throne from Elizabeth to Catherine II (forgetting Peter III's brief stint) was something of a watershed in Russian dynastic history. Russian tsars up through Elizabeth had periodically shown gargantuan appetities in terms of violence, sexuality, lust for power, and byzantine fiscal excess. Russian tsars after Elizabeth began to become progressively more "Germanized", with growing bourgeois instincts, a more pronounced craving for cozy domestic settings, a more metered zeal for displaying wealth, and -- while still sure of their autocratic right to rule -- more restraint in using extreme means. Ivan the Terrible could murder his boyars. Peter the Great could torture the Streltsy and see his own son abused to death. Elizabeth could throw the young Ivan VI into a dungeon for life. From Catherine II onward, these things began to become less tenable as weapons of policy. Few transitions occur instantly in history, and Catherine II was still up to the burden of seeing her husband killed and keeping Ivan VI in prison. Even Alexander I managed to countenance the murder of his father (although the cancer of remorse ate at him throughout his life, contributing to the legend -- and possible truth -- that he faked his death to abandon the throne). But, within a few years of Catherine II's death, the capacity for household violence seems permanently to have passed out of the Romanov dynasty. Where the 18th century in Russia had been the rule of lions, tigers, bears -- and the occasional squirrel -- the 19th century in Russia became the rule of burghers.
I've never been really sure what to make of this transition and when it occurred. How much was the influence of Peter's westernization policies? How much of the French Revolution? How much the shift from Russian tsars marrying Russians to marrying western royals (of which the numerous German states were the most prolific purveyors)? How much the fact that the Romanov bloodline probably ended with Elizabeth?