no, BOI is a scheme which companies can apply for. If you're not sure if your employer is a BOI company or not then best to speak to their HR to confirm.
no, number 1 is saying you can't work on that extension of stay. Number 3 is saying, if you find a job here, that there is the possibility you won't be able to convert to an extension of stay based on employment...at least not without having to leave the country to do so.