Такие cannot be used for plural these and singular this. The closer Russian word to the meaning 'this' and 'these' would 'этот/эта/это/эти'. In a way, yes, 'principals like these' makes sense in English. In another way, 'these' refers to something immediately tangible, something I can point to with my hand. To overcome something immediately pointable in English, we would say 'principals like that/those', but такой/такая/такие is closer to the English 'such', referring to something discussed or conceptualized rather referring than physically present or something towards which I can physically gesture. I agree, it's really posh sounding and unnatural to American ears to say "Schools need such headmasters," but it is closer to the specific use of the Russian sentence. I hope that helps a little?
here you go, that link helped me a lot
Usually adjectives have an ending in two vowels or a vowel and й. But there are also short forms of an adjective that use the usual gender endings instead: ending with a consonant for masculine (i.e. no ending past the word stem), adding -о for neuter, -а for feminine and -ы for plural.
These are most commonly used when the adjective is written after a form of be/is/are/am instead of written before the noun it describes, e.g.
The red book => Красная книга (the short form is not available because the adjective is written before the noun)
The book is red => Книга - красна (short form)
The (singular) neuter short form version is also how to use an adjective as an adverb, which is what is going on here.
Because of директора. Нужно is an adverb which corresponds to the thing which is needed. It's the opposite of English. Basically, "To schools is needed good directors." Examples to demonstrate: "Мне нужен банан." ('To me is needed a banana', need corresponds to the gender/plurality of banana.) "Тебе нужна работа." ('To you is needed work', need corresponds to work.) "Нам нужны яблока." (Here, яблока is plural, 'need' corresponds.) Anyway, I'm not a native, but this is my understanding.