Q1: Certainly. In fact it is now very common. A common vector now is from rogue adverts on web pages exploiting vulnerabilities in the browser or in Flash/Java plugins.
Q2: Also yes. Cross platform tools such as Java and Flash are commonly compromised. It is less likely that malware will target more than one OS but it is certainly possible. There is also malware related to JavaScript and to things like Microsoft Office.
Even when malware is not cross platform, it is still possible for it to travel across OS's by changing files.
2The answer to both of your questions if of course its possible, infact, its the case for most infections. If you suspect your system is infected wipe it and reinstall the operating system. – Ramhound – 2013-02-26T20:18:40.767