Is there any param settings I can change to allow Qubes to be installed on an external SSD?
The Qubes OS.
Simply select external drive as installation destination should be enough.
For booting from QOS installed on external HDD you need to make some changes immediately after the installation.
Check this post for the manual changes to be done in the External USB HDD for it to be bootable.
This info comes from QOS documentation, but better explained in this link.
I have the following structure.
Internal HDD1: Win10+Ubuntu
Internal HDD2: QOS411
External HDD: QOS411
While booting QOS411 from either of these, it works well if I disconnect all other external HDDs. Else, the boot menu entries keep getting botched up.
Hope this helps.