Are there cases where a serious drive-by download attack could crash the operating system or the browser ?
Most drive by attacks work by using exploits. Exploits are often bugs in code, so if they try to exploit one and it doesn't work, then crashing your software or possibly your computer are a good possibility even if the attack itself doesn't get them the result they were hoping for.
If the attack actually works and they get access to your computer, then they can potentially do anything they want, depending on the access level they are able to achieve, up to and including deleting all your files and possibly even breaking the hardware itself if they are particularly clever (such as causing overheating to break stuff).
Yes. This is part of the more general first immutable law:
If a bad guy can persuade you to run his program on your computer, it’s not your computer any more.