High and lofty refer to something that has considerable height. High is a general term, and refers to extending upward or being at a considerable height: high towers; a high shelf. Lofty refers to imposing or even inspiring height, often in architecture or the natural landscape: lofty cliffs; a lofty spire; at a lofty height. These words also overlap in their figurative senses, so that you can elevate or exalt high ideals and ambitions by making them lofty ones.
The act of hectoring someone has many of the same elements as bullying. Hector refers to relentless harassment or tormenting of people, but it consists almost exclusively of verbal aggression—criticism, accusation, and insult—and doesn’t approach the level of cruelty or vicious abuse suggested by bully. Hector is likely to be paired with verbs such as harass, lecture, preach, nag, and harangue. People who hector don’t necessarily have the power advantage of a bully, but they may assume authority or superiority of a moralizing kind.
Both these adjectives describe things that are much smaller in size or scale than is ordinary or normal. Miniature suggests something physically reproduced on a reduced, often tiny, scale: miniature dollhouse furniture; a miniature screwdriver. Diminutive suggests something or someone unusually small (the diminutive size of the phone; her diminutive stature). Although miniature is sometimes used to describe the size of adult people, diminutive is much less likely to offend. In fact, it’s a common word for describing both things and people that are formidable despite being small (diminutive wide receiver; the diminutive pop star).