Betta's wont tolerate a lot of things, including anything that moves much faster than they do (Most species of Tetra, and the barb, and the danio) and anything "conspecific," or "looks like them", so the Gourami would also be "in for it". The results are well documented even on here.
Take the "Catfish" and leave the rest. Not only are the rest not suitable to be housed with a Betta, but they're also in vert strange stocking and numbers. Everything in your friends tank (apart from the Gourami) live in groups of over 1000 in the wild, very strange to see a single Neon, barb and Danio. Infact i would imagine the Barbs aggression is due in part to a lack of friends. I currently have 18 in a 75gal, and im looking at upping that to 24 to spread the agression out a little further.
Once you have the Cory you need to find out what it is, (post a pic and ill tell you) and you'll then need to find it 5 friends, quickly, or he'll be permanently stressed. You can have 6 corys and the Betta in 15gal no problems, providing its not a strange shaped tank? (Corys as above are bottom dwellers, then need space on the tank floor to look for food, so if you have a 15 gal Hex tank, you wont be able to house 6, so no point in even taking the one.)