1. Yes, but you have to go through the lottery (unless the employer is cap-exempt)
2. The H-1B change of status will become effective on October 1, which means that on October 1, your status will automatically change to H-1B assuming that you are in the US in valid status. If, on October 1, you are outside the US or you have no status in the US, then the change of status will not happen, and you will have to apply for admission in H-1B status. You must ensure that your L-1 status is still valid on October 1, which means that you must still be employed on October 1 or you must be in your grace period on October 1. For example, if your L-1 I-94 will be valid until October 1, you could leave your L-1 employer on August 15 and your 60-day grace period would start on August 16 (meaning that you would still be in status on October 1, since the grace period counts as valid status). But if you leave your employer on July 15, this is not going to work.