Let us imagine that I am uploading the application for a faculty position (e.g. lecturer) in a university in UK today. What to expect next? Should I wait for their reply anyway or only in the case that my application is in a short list? How long might it take to get an email from them (weeks, months etc)? Thanks!
In my experience English and Welsh universities will notify all applicants shortly after the shortlist has been decided upon, either with a positive or negative response. Moreover, this decision is typically quite fast, around 2weeks - 2months.
 I have insufficient experience with North-Irish universities, and have applied to Scottish universities and never received a response at all.
Normally, shortlisting happens a week or two after the application submission deadline. If you are shortlisted, you will be invited to an interview. If you are not invited to an interview within a month after the application deadline, it is safe to assume you are not shortlisted, but the University does not want to let you know until the appointment is made (which may happen a few months later).
The interview can be scheduled from a few weeks to a few months after the shortlisting date. After the interview, the decision is normally made within a week. If you don't hear from them after 2 weeks, it is safe to assume you are not the first candidate, but the University does not want to let you know until the appointment is made.
It is not unusual to never hear back from a University if your application is unsuccessful. Generally speaking, standards for professional communication in the UK academia are surprisingly low.