Can doctor note be used as a referral to a specialist ?

The requirements of both specialist offices or third party insurance vary. A note suggesting you see a specialist would not meet the referral /documentation requirements in many instances. A formal call from the referring physician to the involved specialist or a paper trail created by their office staff is the usual practice.

Yes, if including in recommendations seeing a specialist. Some other times, a referral is initiated at the time of the office visit and that can be checked with the respective office.