According to Merriam dictionary, that has many usages, but those that I was interested in, and the examples are about are:
- as relative clause
- as conjunction to introduce a subordinate clause
In general, we can always find what "that" refers to. In the cases above it could be a thing, person (in relative clauses) or a sentence (in subordinate clauses)
So let's analyze the sentences,
The students who were absent, that I prefer not to mention their names, should do this practice...
Here that (in my intention) refers to the apposition "I prefer not to mention their names"
While the main clause for this clause is absent, the closest words I found for such structure are which or thought:
The students who were absent, which/though I don't want to mention their names, should do ...
I think the word I was looking for could be though as it is in Persian Har Chand or Har Chand Ke (something like How-ever-that) and it's probable that we shorten it in such occasion to Ke which corresponds to which and that (and now though)
if that points to the students then the correct sentence is
The student who were absent, whose names I prefer not to mention, should do this
In case 3 "that" was extra positioned, and the correct sentence could be:
- you said that I can't catch you, but ...
I feel we do extra position in Persian to put emphasis on something, however it is also odd in Persian too.
In sentence 2 and 4, that could refer to the clauses "a car suddenly stopped in front of us" or "he came"
Here, we said about something surprising (suddenly...) then "that" can make emphasis... or maybe it is like when to point the coincidence, or even then to show the result
I also know that can be used to express the result or purpose of something like (From google):
expressing a reason or cause. "he seemed pleased that I wanted to continue" expressing a result. "she was so tired that she couldn't think" expressing a purpose, hope, or intention. "we pray that the coming year may be a year of peace"
expressing a reason or cause.
"he seemed pleased that I wanted to continue"
expressing a result.
"she was so tired that she couldn't think"
expressing a purpose, hope, or intention.
"we pray that the coming year may be a year of peace"
The case 6 is similar to expressing a result...
In all the other sentences, that refers to a sentence or clause. (And it is not much odd in English too)