When 있다 is used only, it means 'being in somewhere.' But when using with other verbs, it plays auxilary verb role to represent tense.
So '있어요' means that staying right now for example "나 집에 있어요=I'm home."
But when using other verbs such as '고 있어요', '고 있었어요' are presenting different tenses. For instance, "나 밥먹고 있어요" is present progressive like "I'm eating." And "나 밥먹고 있었어요" is past progressive such as "When I got there, he was eating".
어요,아요 and 애요 are all used for present tense, so these aren't replaced with "고 있어요 and