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If you run a program written with .net, you need to have installed the correct version of the .net framework, the one that matches the version the program was written with.
That is what I was told quite a while ago. So going by what I was told then the answer to your question is yes for all net framework versions to be installed.
The .Net framework supports applications written to interact with that particular runtime. So yes updating to the most recent version is advisable but not crucial dependent on the apps installed... if it asks for a particular framework then that's the only time it needs to be installed.
I have several versions installed, all were specified by programs I installed and run but were either included with the program or automatically downloaded from the 'net. Version 1.x probably is no longer needed. I've found programmers have been very good about listing the need on their site or having a prompt in their program to check for the presence of the needed version or prompt to get it if not already installed.
4.7 includes all of the .NET versions prior to it. You should be able to just install 4.7 and be done with it.
There are occasions where a particular piece of software will ask for a specific .NET version, and you may have to install that version to get the software to work, but that would be a rarity, I would think.
Some software will include a specific .NET runtime if required to get the software to work, and it may install with the software, so don't be alarmed if you are looking at the installed software listing in Windows and see other .NET versions there. They may have been added by programs that you have installed.