*A/V + (으)ㄹ 거예요 : This pattern is used for the future tense. Even by native Korean speakers, the 거예요 is often mispelled as 꺼예요.
To make the low form (반말), the 예요 part becomes 야: A/V+(으)ㄹ 거야
This form is originally from A/V+(으)ㄹ 것이다: A/V+(으)ㄹ 것이다> A/V+(으)ㄹ 것이에요> A/V+(으)ㄹ 거예요
*Verb + (으)ㄹ게요 : This pattern is used for the future tense. Even by native Korean speakers, the 게요 is often mispelled as 께요.
This pattern is restricted to first person usage.
To make this the low form (반말) simply drop the 요 ending.
This pattern can only be used as a statement and cannot be used as a question.
This pattern must be used in a way to where the other person you are speaking to is somewhat related to the situation you are describing with the verb. "I" must be the subject of the action (though it is also acceptable for suggestions where it can also be "we").
This pattern should be used when the action relates to the listener(s) directly or if it's for the listener(s)' sake.
*~(으)려고 and ~(으)려고 하다 are used with action verbs to express a plan or intention. ~(으)려고 makes an incomplete clause meaning “In order to…” or “With the intention of…” ~(으)려고 하다 makes a complete sentence that can show intention for action or a possible state of the near future. ~(으)려고 and ~(으)려고 하다 are not used with suggestive or imperative sentences.
*Attaching ~고 있다 to the stem of verbs gives it the meaning of “I am ____ ing,” – as in, I am currently doing something. It is called the “present progressive” because the action is being done in the present, and is currently “progressing” as time goes on.
잘거야 is informal form of 잘 거예요.
잘게 is informal form of 잘게요. 잘깨 is wrong form of 잘게
잘거야 means "I'm going to sleep"
잘게 means "I'm going to sleep now"
자려고 means "I am planning to go to sleep"
자고 있어 means "I am sleeping"