I don't play on PC myself but if I understand the process correctly if you purchased or redeemed the game on one Origin account that game will be tied directly and solely to that particular account; while you could sign into your account on any computer it would only be available on your Origin account; and two people cannot be signed into the same Origin account at the same time since it will want to logout the older session.
As far as the game operates there is no way to "restart" or otherwise clear out your progress as far as I am aware. This is a game that you really can't "mess up" or make the sort of major error or mistake which would prompt a wholesale restart; in fact it's really not preferable because the goal of unlocking the various character variants, accessories and areas all represent a substantial investment of time and effort which I doubt anyone would want to discard in order to start over.
You should find that you have access to all of the default character on both the Zombie and the Plant teams; you can change your character by entering the Dressing Room which you will find to the right side of the main gate when you are facing it. Changing teams can be done by going to the little 'recruitment' desk which is positioned on the left side of the main gate.
If you have any other general questions I might be able to answer them since the game play is universal across platforms; only the actual control schemes will differ.