Hi There. Do I send Schedule K-1 at the same with form 1120S? Also, the same would be applied with sending Schedule K-1 with the form 1040 for personal tax filing? Thanks

Yes - The K-1s are filed along with the S-Corp return (1120S).
No - The K-1s do not have to be attached to the 1040.  You should only attach your Schedule K-1 if there was an amount of income tax withheld and remitted to the IRS or state on your behalf.  Otherwise, no need to attach the K-1.