Well the first thing that comes to mind is, you need a heater.
Unless your room temperature water is between 75F to 82F your Betta will be cold.
Another important point is you cant have the temperature change all the time.
for instance if your keeping the tank in a room where you use an air-conditioner or a thermostat.
it will effect the water temperature too.
You said it right : Betta fish are also called fighter fish for a reason, they need to be alone or they will kill the other fish. and also you need some sort of lid or they will jump out.
some other things you should know are :
The Betta needs to be feed once a day, only what it can eat within 5 min. if the fish looks really bloated, you know its had more then enough. if you feed it to much it might over eat so much it dies.
You need to clean the bowl once a week if it has no filtration. It helps if you keep around a plastic water jug to pretreat water for the weekly cleaning. This will also have it ready at room temperature.(but make sure its clean and always soup free) and remember not to scare the betta with a sudden water change.. do it slowly..
DON’T place the bowl in direct sunlight, or near a cold vent or draft. it will play with the temperature.
About adding the plants, and other ornaments, It is always safe to add new aquarium safe decorations as long as you per-rinsed them first. ohh make sure the ornaments don't have any sharp edges, Bettas are very delicate. they will get cut easily.
one last thing.. I do not know if you got live plants or fake ones. Bettas love real plants! they add oxygen to the water and they reduce ammonia.