Experience letter is needed if it qualifies you for a certain GC category. For example, if you are filing under EB-2 using 5 years work experience as the basis, and that 1 year tenure is part of your qualification, then it is required.
Yes, you can get letter from supervisor or colleague on their personal stationary or their current employer's letterhead, that can be used as well. You should also submit a copy of their linked-in profile which shows overlap at the old employer. Discuss with your attorney about exact format of letter.