I have obtained the email address of the HR from my senior (friend) interning at my dream company. As I am also keen to intern at the same company this coming May, in my writing of email to the HR, should I briefly mention about my friend who gave me the HR's email address? Really appreciate advice and thanks!
You should make sure to check with your friend if they're okay with using their name in your message. If it's okay, briefly mention it at the start of the email like this.
Dear [HR Person Name],
[Friend] provided me with your contact details, and I'm writing you to inquire about an internship at [Company Name].
The usefulness of this differs depending on whether it's a small company where most people know each other or a large multinational with 1000s of employees across multiple offices. In the second case, HR will probably not know who your friend is and it will not really add value.
Another option could be to ask your friend who works there to recommend you directly to HR. This way, that colleague vouches for you and that can definitely be advantageous.