"I am a singer."
에요 is the verb - "to be". It is a different politeness level than "입니다".
The verb is 이다 by it changes when you ad it to nouns. For example when. The noun ends in a vowel it changes to 예요 but if the noun ends in a consonant then it becomes 이에요
-예요 is the copula (- 이에요 after consonants), and it means is, are am. So it'd literally be "I singer am."
예요 is a contracted form of 이에요 which is the polite form of 이다 if I recall correctly.
It's in 는, because 저는 means "I am". The verb "to be" is irregular in a lot of languages
Not exactly. The verb is 이다 which becomes 이에요 or more easily 예요. 저는 is also not "I am" but more like "as for me"