Can I boot an hdd with windows 7 without altering the original windows 10 environment?

It depends.  Every installation of windows is highly customized to match a particular configuration.  You say you have Windows 7, but what computer was that windows 7 on?  Was it on the same computer that boots Windows 10 now?  Did you not make ANY hardware changes or upgrades to the windows 10 computer, compared to when it was running windows 7?

In general, it would be highly unlikely for a windows 10 computer to boot perfectly off of a windows 7 external drive.  This is because if you HAVE a windows 7 external drive, then you've probably changed hardware (or the whole computer) a few times since you were running windows 7.

Having said that, it won't harm anything to try to boot the external drive with windows 7.  It will either work, or it won't...but it won't alter windows 10.

No, Windows can be installed in C drive only...therefore only one Windows can boot.

You can install Virtual Box software. Then make a virtual computer in it. Finally install Windows 7 on virtual computer.

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If you installed win7 to the external HDD using that computer, you should be able to boot it.

If they're on different hard drives, and are both complete installs, then yes you can.