Yes. All .NET Frameworks can coexist on the same computer (versions 1.1, 2.0, 3.0, 3.5, 4.0). Each version of .Net is a complete runtime package. One version is not dependent on the other versions and will not interfere with other co-installed versions. If you are installing a newer version, it is recommended that you keep to old version installed -- you may have other programs that need it.
You must have the exact .Net version that is listed as the program prerequisite. So for example, if the program prerequisite is .Net 3.5, you must have 3.5 installed. In this example having .Net 4 installed won't help a program targeted to 3.5.
The .NET Framework 4 Client Profile is a subset of the .NET Framework 4 Full version. You can install either one. The Full Framework 4 has server libraries only needed for computer servers. It is a larger download (About 25% larger than the Client Profile. Varies by your system OS edition.).