New computer

If the installer ran without issues, then no need to install the latest combined (i.e. 2015-2022) VC++ redistibutable packages as you have the required ones already installed. But I always recommend installing both x64 and x86 versions.

The ini file you attached is an initial ini generated by FSUIPC for an unlicensed version of FSUIPC7.
Do you have a license? If so, you can either re-register (you will have to re-install to do this) or copy across your FSUIPC7.key file to your new computer. And also, as I said, you need to copy your FSUIPC7.ini file (as well as any other files you may use) from your old PC to the new one as well, if you want to preserve any settings. Once you have done this, then run FSUIPC7 and this will update the .ini with the new device information and add new entries to the [JoyNames] section. It is this that will need editing.

Just can't register FSUIPC7 with existing key. It says that it's not a valid

Bought another FSUIPC7 in simMarket. To register added the key to FSUIPC7, which was registered. While trying to register WideFS (bought in simMarket in 2014 with another email) it told that it's not a valid registration for WideFS. 

Checked box that inform if I was using a different name or email for WideFS

WideFS Name: WideFS (is it correct?)

WideFS email (the one that I bought WideFS)

Posted by: @eduardop

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Just can't register FSUIPC7 with existing key. It says that it's not a valid

This is the error you get if you do not have the correct VC++ redistributables installed (or if the key details are incorrect...). Install the latest combined VC++ redistributables for both x64 and x86 and try again.

Posted by: @eduardop

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Bought another FSUIPC7 in simMarket.

You didn't need to so that if you have already purchased a key for FSUIPC7...

Posted by: @eduardop

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WideFS Name: WideFS (is it correct?)

No. It is your name, or the name you used when purchasing the license, available in your simmarket account (as is the email used and key).