Do letters from friends and family about our relationship need to be handwritten and notarized?
In the spousal visa process, the USCIS is trying to determine that you have a bona fide marriage. And, if you have just recently married most people understandably don't have many of the typical bona fides, such as a joint checking account, a joint lease or mortgage, joint health insurance, etc. These are the kind of things that typical married couples would have to show that you have intertwined your lives.
So, if you're newly wed you typically don't have those things yet. So, you're left with getting these sworn 3rd-party affidavits from people who will attest to the relationship. These aren't official documents and aren't on an official list. They are just what we, and others in the industry, have found can be effective at establishing the relationship.
Regarding having them notarized, yes - they should be notarized. You are already lacking other bona fides, so the last thing you want to do is make a weak case. You want to spend the extra time and money (if necessary) to get the affidavits notarized. Now is not the time to look for short cuts or skimp on the evidence. It doesn't need to be handwritten, but it should definitely be notarized.