I would say that is a common abbreviation for "-que". Maybe you could find useful Cappelli's Dizionario di Abbreviature latine (a very detailed repertory of latin abbreviations). Take a look here.
Here is the phrase with the soluted words:
silensq(ue) sisto tuumq(ue)
I would add that this is not a ligature but an abbreviation, while -st- of the word ...
The modern German roman-type ß was developed at the end of the 19th century as an analogue of the blackletter ß, which was a ligature of ſ and z (which is reflected in its name) that had slowly acquired letter status and looked distinctively different from your ſs (more like ſʒ). Some of the new ß designs may have been inspired by your ſs and similar forms. ...
It must be que.
The conjunction -que is very common in Latin, and it is no surprise it has it's own symbol.
For example suumque is (almost) the same as et suum and means "and his own".
The excerpt you have is a fragment, and the exact translation depends on more context.
Here is a partial answer.
I don't know what kind of forms you can find in historical (e.g. medieval) documents.
In normal current typographic practice, no
In Latin texts that have been published in the present day by academic sources, you're unlikely to find ligatures of any kind. It's currently preferred to write "oe" (or "ae") as a ...