Allow a margin of difference of

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 example:

But it would be a surprise if the presidential election scheduled to take place in Venezuela is allowed to threaten the position of the country’s dictator, Nicolás Maduro.

You are right to assume this is a type 3 conditional, according to the classifications in your book. If the Economist writers were following the strict rules that your book proposes, then the proper way to write this sentence would be:

But it would be a surprise if the presidential election scheduled to take place in Venezuela were allowed to threaten the position of the country’s dictator, Nicolás Maduro.

I would have written it that way, although as your text pointed out, many English speakers would have written was. Still, I don't think most speakers would combine "would" with "is." I'd say it's a grammatical error. Either "will" with "is" (which would make it a type 2) or "would" with "were" (which would make it a type 3) is much more correct here.

Your second example:

Finding a viable way to mine outer space’s plentiful supplies of platinum, for example, would surely lead to a meteoric descent in the price of the metal.

This is another form of the type 3 conditional, although your book doesn't seem to cover it. The first part isn't worded using an "if" statement, but a gerund phrase like this, followed by "would" is another proper way to describe something imaginary. It could be reworded like this without changing the meaning, at all:

If we found a viable way to mine outer space’s plentiful supplies of platinum, for example, it would surely lead to a meteoric descent in the price of the metal.

Note that you can also use infinitive constructions this way: "To find a viable way . . . would surely lead . . . "