Tetra recommends that you do not split a bottle. I think this is probably due to not knowing that the bacteria is evenly distributed within the bottle. And while I don't recommend splitting the bottle, to answer your second question, there is an expiration date on the bottle.
It won't be an issue if you use too much BB. I did read somewhere people day that TSS will expire approximately 6 months after the bottle has been opened, just one issue with that, TSS for some reason doesn't come with a safety seal so you never know 100% if the bottle has been opened or not.