Since my friend is out of time to go to immigration, can I go immigration and apply for my friend?

Applying for a C of R or a Visa Extension isn't like a 90-day report, which anyone can do you your behalf without a POA or any other special document.

If the OPs friend is in hospital or otherwise medically unable to travel to the Immigration office, then a doctor's letter should work, along with a limited Power of Attorney (English language OK) to give the OP the ability to apply for his friend. Ideally, the medical letter should be on the letterhead of a well-known local hospital, not a small private clinic.) Also, they'll want to see a photo of the applicant looking really sick, in his hospital bed, surrounded by nurses in uniforms.

If the OP's friend simply doesn't have the time to be bothered with going to immigration, then I suggest s/he apply with their local consulate. Service is much quicker, but you pay for the convenience. The Americans must make appointments on-line, but you're seen promptly. In-and-out in less than 15 minutes.