No, it makes no sense in English.
Here are some correct sentences:
Are, and drop the "for"
The sentence, "They are going to the beach." is correct.
I would say; She's going shopping. Or She's going grocery shopping. We don't want to be too wordy.
If your going shopping, it means you plan to do some or are on the way to the shops. If your doing the shopping, it means you are actually shopping.
Only one sentence is correct. The correct sentence would be "He saw me going there".
The sentence "are you going with dad and I" is not correct. It should be "are you going with dad and me" since "me" is the correct pronoun to use in this case.
I am going shopping and after am picking the kids from school.
What are you going to draw? It is correct.
No, the correct interrogative pronoun is "who", the subjective form:"Who is your mother?"The pronoun "whom" is the objective form, used as the object of a preposition:"To whom do I send the letter?""For whom are you making a cake?""With whom are you going to the movie?"
"Steve and I are going" is correct. Use "I" as the subject of a sentence and "me" as the object. In this case, "I" is the subject performing the action of going, so it is the appropriate pronoun to use.
Yes, perfectly correct.
Whether you are using the contraction I'm, or the long form, I am, this would appear at the beginning of a sentence or a phrase within a sentence, and not at the end. Here is a normal sentence: I am going shopping. If you instead were to say, Going shopping, I am, you wind up sounding like Yoda. And if you said going shopping, I'm, that would sound even worse. As an answer to a question it would sometimes be possible to use "I am" as a complete sentence. Who is making that noise? I am. That works. But you would never say "I'm" as a complete sentence. That would not sound right, even though it technically has the same meaning as the long form.