(Might be making some of this up, background info in English is surprisingly sparse. Would be nice if the prequel manga got translated, at least.)

I believe I heard somewhere that the pests always existed, but suddenly went berserk (about a thousand years ago?), and the Flower Knights had to be formed to combat the threat. They originated in Blossom Hill and formed the Fos Knight academy for that purpose. The other nations have their own royalty, nobles, knight order, etc. to also help in the fight against pests. Every nation also has a World Flower at its center.

I feel like it'd be easier to break down the relationships between the characters per nation...

Off-hand, I know Rosa Novalis is the queen of Winter Rose, who has Black Baccara and Dendrobium as advisors, and Royal Princess (Rose Diana) as her vassal. The Cattleya mansion was built to contain Cattleya, who was considered too dangerous and unstable at birth, but Baccara chose to lock her up instead of outright killing her in the hopes that she could learn to control her power. Dendrobium also stepped down from her position as king's advisor to be Cattleya's caretaker, before taking up mercenary work. Oncidium (Orchid Wydler) and Cymbidium are just two girls that ended up being Cattleya's maids/playmates. Speaking of Oncidium, we know that some pests are sentient, and still others like her pet Maidoari (who she adopted during Lavender's event) are benevolent.

In Banana Ocean, Casablanca is the queen there, with Mountain and Star Lily as her advisors.

Bergamot Valley and Lily Wood are trickier, since they border the land where the pests originate from and their hierarchy doesn't seem as clear (Lily Wood seems to have a senate?). Lavender in particular spent her childhood in Bremen, but presumably had to relocate to Bergamot Valley after the city became overrun with pests. Beyond that, we know that Edelweiss is a noble from Lily Wood, and Snowflake is her maid.