There is absolutely no grammatical reason to avoid starting a sentence with these adverbial phrases: as I noted in my comment above, all of your query sentences are well-formed and idiomatic.
Stylistically speaking, such phrases are useful devices for creating a context for the subsequent description that is a little more sophisticated and nuanced than the effect which would be produced by straightaway leading with the main point.
For example, your sentences 3) and 4) immediately present the reader with the point of view of the writer/narrator.
Taking 4) as an example:
On the pretext of watching a Saturday night show, I lingered in front of the TV until 11.30 p.m.
from the outset, it is clear that somewhere in the situation that is being described, there is a motivational conflict. At this point we don't know whether it is an internal one (perhaps the narrator knows she should really be studying instead of watching TV), or an external one (her friend has invited her to a party she doesn't really want to attend, and she is trying to put off going out for as long as she can) -- but in any event, the way the sentence starts immediately sets up certain expectations in the reader regarding a conflict that will become more explicit later on.
Contrast this with a more basic treatment:
I lingered in front of the TV until 11.30 p.m., watching a Saturday night show.
This conveys the same information about the narrator's actions, but reveals a lot less about her state of mind. Here, the only clue to the latter is the use of lingered instead of a word with more neutral connotations like remained.
To sum up, this example illustrates how a fronted adverbial phrase can serve as a device to introduce suspense into a description.