You're quite right: as it stands, the second clause implies that as a result of failing to learn English they do reach the 'target stage'!
This is a very tricky use of negatives with ellipsis. What the writer intends is something like this:
They don't learn English at all
and
(they don't) reach the target stage.
But this doesn't work. The expression at all is what linguists call a 'Negative Polarity Item': it is only used in negative contexts. In this sentence it combines with the not in don't and so to speak "absorbs" its negative sense before you get to the second clause. Consequently, that not cannot take the second clause into its scope. The parse looks something like this
They [do not at all] learn English
and
(they) reach the second stage
You have a number of options for correcting this. One is what you suggest: adding a negative expression to the second clause. This Since the negative in the first clause is comprehensive, not at all, a good choice for the second clause would be the equally comprehensive never:
They don't learn English at all and never reach the target stage.
That would be parsed something like this:
They [do not at all] learn English
and
(they) [ never ] reach the target stage
Another option is that suggested by snailboat: employ the 'exclusive' coordinator or instead of and, and pair the NPI at all with a corresponding NPI in the second clause
They don't learn English at all or ever reach the target stage.
They don't [at all] learn English
or
[ ever ] reach the target stage
Finally, you could coordinate learn English with reach the target stage using or, and move the NPI at all to a point where it modifies the coordination:
They don't learn English or reach the target stage at all.
(learn English )
They don't ( or ) at all.
(reach the target stage)
ADDDED:
Your second sentence, "They can not write English sentence correctly and speak out their feelings in that language", is marginally acceptable; there's no ambiguity about the scope of the negator. But it would be better expressed with or, which alerts the reader to the fact that what follows falls under the scope of they cannot:
They cannot write an English sentence correctly or speak out their feelings in that language.
Your first clause is using inversion without the word if. You can only do that to form conditionals if you use subjunctive inversion, which you are not doing here.
- *Is it twice as much, (then) we call it 2 G. [wrong]
- If it is twice as much, (then) we call it 2 G. [right]
- If it were twice as much, (then) we would call it 2 G. [also right]
- Were it twice as much, (then) we would call it 2 G. [also right]
Only the last version there permits you to forgo the if by virtue of using subjunctive inversion.
There are many other ways to form conditionals, but what you have written is not one of them.
Best Answer
An alternative to Sovereign Sun's use of as or since is to express the two tiers of reason with and:
This has the advantage of putting the key point on the left end of the sentence, the more emphatic 'new information' position.