For the most part, HPs are what you are concerned with if your identity has been compromised. SPs are typically done on existing accounts and for internal monitoring by creditors, promotional offers, personal credit monitoring and insurance.
The definition of a so-called soft inquiry is that it is not available to any party other than the named consumer.
Thus, a soft inquiry may be of record with a CRA, but will not "post" to any credit report obtained by anyone other than you.
No, soft inquiries are not seen in real or any other time by others.
There's also other database and reporting services used by a variety of institutions that include Lexis Nexis, Sagestream, etc.
Inquiries report instantaniously. As in within a second or two. I once applied for a card and while the card app website still showed it as "loading/processing" I got an email from credit karma saying that I have a new inquiry. So before the app even finished processing I already had the inquiry and CK even had enough time to send me an email about it.