The continuation using "and" is fine in all three constructions. Good job putting the comma between the clauses in the middle one. As an aside, I would either say "I have been learning English for six years" or "I have studied English for six years."
ETA:
You edited the title to add "should I and is it one clause or two?"
Should you? Yes, it is fine.
A clause has a subject and a predicate (note, sometimes a subject is "understood" such as in the sentence "Be careful" where "you" is understood). If a clause can stand alone as a sentence, it's an independent clause.
In the second sentence you have as an example, it is a compound sentence: two independent clauses joined by a conjunction.
In your first and third sentences, you have just one clause with a compound predicate because the additional predicates share the main subject. The added bit in the third sentence is an additional direct object of encounter (...encounter problems and issues).
A note on your "should I" question: although you can keep putting independent clauses together "forever" by joining them with coordinating conjunctions, it becomes tiresome after a while. I think that's true in German, too, though, isn't it? :-)
As to supporting evidence: Here is a webpage with some info on the difference between a compound sentence and a compound predicate, but I think you are more interested in clauses, so here is another pages that has perhaps a little better explanation of compound sentences and clauses in general, though it doesn't mention compound predicates at all. I couldn't find a page that I thought had a good description of both.