Kingsley Shacklebolt is still Minister for Magic in 2014. He was elected after being ‘caretaker Minster’ following the Battle of Hogwarts.
Pius Thicknese apparently didn’t face any punishment after the Battle of Hogwarts, as he was under the Imperious Curse and not responsible for his actions. He’s omitted from the official Minister for Magic records.
The Potter and the Weasley families always just give their children the names they like and it’s not for magical reasons.
Some wizarding families still follow the ancient practice of consulting a Seer to know their child’s future so they can name them appropriately. Though the Blacks were named after stars and constellations, which suited their lofty ambitions and pride.
Dolores Umbridge was born 26th August, she was a Half-blood (she had a Muggle mother - who she hated), she had a Squib brother (who she hated), her father worked for the MoM in the Department of Magical Maintenance (which she was ashamed of), and she could never find any man to marry her.
She had a Birch & dragon heartstring wand, and she was a Slytherin (not a shocker!). Most wizards just pretended to believe her lies about her lineage because they were frightened or intimidated by her.
The Death Eaters sensed she was as bad as their worst and so let her have more power in the Ministry under Thicknese. After Voldemort’s death she was tried and sent to Azkaban for torture, imprisonment and the deaths of several Muggle-borns (they didn’t survive their stay in Azkaban).
J.K. Rowling says Umbridge is on the same level as Bellatrix Lestrange and Lord Voldemort.
Azkaban (a place created by Dark Magic) was converted to a prison in the 16th centuary because it was abandoned, isolated and already infested by Dementors. It had been there since the 15th centuary, but had been built by an insane wizard who used it to lure Muggle sailors so he could torture and murder them. He had used concealment charms to keep it hidden the rest of the time, only after his death was it visible to wizards.
After the Battle of Hogwarts, Kingsley Shacklebolt purged Azkaban of Dementors and put regularly rotated Aurors in charge. There’s been no break-outs since.
Sybil Trelawney was born 9th March, she’s a Half-blood (Muggle mother), she has a Hazel & Unicorn Hair core wand, she was a Ravenclaw, and when younger she had a very short marriage that ended after she wouldn’t take his stupid surname. She’s a 90% fraud as a Seer, she just plants the idea of things in peoples heads and they self-fulfil the prediction.
Before Hogwarts she got infrequent jobs (only ones she thought suitable for a Seer) by trading on the famous name of her Seer ancestor. Professor Trelawney felt inadequate which is why she lied about her gifts to everyone, why she has a drink problem, and why she didn’t spend time around the other more talented staff.
Rufus Scrimgeour was personally killed by Lord Voldemort
A number of past Ministers for Magic have descendants at Hogwarts or in the Death Eaters during the series - Rowle, Lestrange, Diggory, Parkinson, Flint, Boot, and Fawley.
Thestrals are only found in the British isles, Ireland, parts of France and the Iberian Pennisula. Other parts of the world have their own equivalents to Thestrals.