- As for emphatic sentences, to my mind there isn't much difference in the following
Такая жара! (Such hot weather we are having!)
Какая жара! (What hot weather we are having!)
2 Он такой яркий, что я не могу на него смотреть.
We have an adjective in the full form, so for the emphasis use the full form of "такой".
Though It's impossible to use "так" to emphasize a full adjective, you can use it before a short form, but you can't use "такой" here.
Он так ярок, что я не могу на него смотреть.
3 For the emphatic meaning of "How + (adjective/adverb) !" in English, can only "какой" be used?
It depends on what exactly comes after "how", in case it is a full adjective, you use "какой"
Какой обидчивый!= How touchy.
If you have a short adjective, use "как"
Посмотрите, как (он ) обидчив!
If you have an adverb, also use "как", "так".
Как плохо! Так плохо?
"Плохо" is an adverb. Not a noun, so "какое"and "такое" are impossible.
Такое/какое can be used either with full adjectives or nouns in the neutral gender.
Какое/такое горе! Какое/такое огромное!
Ask the last question separately , because it has nothing to do with the emphasis.