Good question! Because Japanese originally has the word "kyō" for "today", and 今日 in (ancient) Chinese also means today. Japanese adapted Chinese characters (so called Kanji in Japanese) later, making this word pronounced "kyō" but written as "今日". There are some words in which the pronunciation is not related to the individual Kanji, but don't worry, such words are limited in Japanese. If you want to learn more, these words are called "熟字訓／じゅくじくん/Jukujikun" in Japanese.
Due to the number of homophones in Japanese, short words like this can mean several different things. Without either kanji or context to help define, I don't know if it wants sutra, interest, misfortune, or today. Even if the kanji is not the focus of the lesson, just having it there can do a LOT to help ground and reinforce learning words in Japanese.
The う after the sounds u and o makes it longer. The same happens with い and the i sound and the e sound. And with あ and a. So in this case きょ and きゅ are short and きょう、きゅう are long. Also, the small よ、ゆ、や after an i sound eliminate it doing the last consonant be followed by a y.
By "shorter" and "longer" do you mean the vowel sound changes some (like how english long and short vowels sound different) or do you mean the length of time you say the vowel changes? I've seen a few people say the う makes the vowel longer but I'm not toally sure which they mean.
It means time duration. Technically long vowels in english are not long vowels but diphthongs, historically they were, but as you can see from your orthography, the language has evolved but not actualized its terminology. In japanese, the vowels are still long in its original definition: Time. Actually, when learning a new language, always think of length as time, not as quality except you're told otherwise.