Yeah, I wouldn't give him any tankmates, you can try some ghost shrimp if you like or red cherry shrimp although they might become snacks later on
but it's something you can do.
When measuring fish we actually don't include fins, well not on Betta's at least. so you're measuring from nose to peduncle which is the start of the tail/end of the body. So you're probably looking at 4-6 weeks old in which case. And just want to make sure you know; babies need to eat 3-4 times a day, small but frequent meals. They also need water changes at least around 50% every day/every other day to keep him/her from being stunted. Babies excrete a growth stunting hormone that in the aquarium, backfires on them so you have to physically remove it by doing water changes.
And also, a cycle won't happen in a few day's, the Nitrogen Cycle takes just about a month to complete but with so many water changes being done for your baby, you don't have to worry about it for now