can i install both quartus14.1 and 13.1 in64bit win7?

Yes, you shouldn't have any problems. You need to ensure that they go into different directories, of course.

Have multiple versions of EDA tools is quite common, as some projects may require specific tool versions.

There should be no limit on the number of Quartus II version installed in your PC provided your have enough disk space. I have 4 Quartus II version installed in my PC and they are working fine.

Nope, you need to refer to the readme file on which OS is supported for different version of Quartus II. I would personally advise you always you the latest version because it fix a lot of old bugs.

Just to mention, the latest version depends on the device being used, as with more recent versions device support for old families disappeared.

Found the link to Altera webpage which talk about the Quartus II OS support from other thread. Hope it is useful.