1. Flash exploits effect all operating systems, however as long as you do not run a webbrowser running flash as root or an admin user they can only cause minimal damage.
2. The standard MS office exploits are due to their proprietary code base and scripting, since the open alternatives use another code base and do not run MS office scripts there is very minimal potential for office exploits to effect you.
3. All software has exploits and vulnerabilities, it is the nature of objects created by man, they are inherently flawed as are the creators. When running open source software you get the benefit that many eyes can see the code and use it for free, which allows for faster discovery and remediation of vulnerabilities. On the other side of the coin some may argue that open source software is weaker because the hackers can also review the code to find the vulnerabilities faster, this is true, but since the development teams are larger the good guys can find them in the same time line and remediation is also much faster.
To learn more about security you can checkout http://www.sans.org/ .
To view security vulnerability history for multiple platforms and software you can checkout http://www.securityfocus.com/
One thing I have noticed from watching securityfocus for many years is that proprietary software such as MS Office suffers from many remote exploit vulnerabilities which allow hackers to run commands and software on your system, but their open source equivalents generally only have denial of service vulnerabilities which would only allow an attacker to stop the program from working rather than taking it over or using it as a gateway to your system. However it is up to you to do your research to determine the right balance of functionality, security and price for your needs.