One way to tell if you're at best friend status with an animal (and thus able to get their photo), is they can come up to you and ask to change their greeting.
Sending letters is pointless apparently.
Furniture is the best daily gift for raising friendship, doesn't seem like it matters what it is.
And anything that sells for 2500 or more is ideal when trying to get a photo in return.
Wrap everything for more friendship points!
Gift wrapped non-native fruits are wonderful birthday presents. (The guide says coconuts are best, but according to how they list things, those should only be a Tier 2 birthday present)