A Serene Highness can be higher than a Royal Highness under certain circumstances. For instance, Prince Albert is a Serene Highness but he most certainly ranks higher than, say, the Duke of Cambridge or the Prince of Wales. A Serene Highness who is not Head of State or his/her spouse is indeed usually lower in rank than a Royal Highness from a different country. However, they may be (and are) quite a few exceptions.
Excluding Majesties (Royal and Imperial), the ranking among Highnesses is usually like this:
- HIH (His/Her Imperial Highness)
- HRH (His/Her Royal Highness)
- HGDH (His/Her Grand Ducal Highness)
- HDSH (His/Her Ducal Serene Highness)
- HMSH (His/Her Most Serene Highness)
- HSH (His/Her Serene Highness)
- HIIH (His/Her Illustrious Highness)
There were also oddities like HEH (His Exalted Highness used by the Nyzam of Hyderabad), HSH (His/Her Sultanic Highness used by the son, daughters and daughters-in-law of Sultan Hussein Kamel of Egypt) and HMEH (His Most Eminent Highness).
As for bowing/curtseying between Heads of State, you are correct that it is not needed (and certainly not required) at all. Sometimes, elected Heads of State may opt to bow/curtsey to monarchs, especially female or a generation or two older than them, but it's entirely up to them. For instance, I seem to remember President Obama bowed to Emperor Akihito but it was not because of Japanese traditions and culture (the Emperor bowed back). I have also seen various US Presidents bowing to Queen Elizabeth as a mark of respect - although they most certainly didn't have to.