Translation:She travelled to many countries by means of Esperanto.
So, let me see if I understand this. Per already means by means of. So pere de seemed completely superfluous. So I looked it up in PIV, and it apparently means something more like thanks to. In other words, it is the figurative sense of per; obviously you don't travel by Esperanto the way you travel by train. But you might not have been able to travel without it. Am I understanding this right?
And if I am... does that mean that one shouldn't use per in this figurative sense? Or is pere de just an optional way of making it clear this is what you mean?
And, just out of curiosity, is there any kind of logical reasoning behind this distinction from a grammatical perspective, or is it pretty much just an idiom? It seems to me you have taken a preposition which is already inherently adverbial, then added an adverb ending and another preposition rather arbitrarily. Any comments on the etymology of this?
Pere is the adverbial form of per a preposition with meanings like: "By means (or good offices) of, per, through, with, ktp." You might occasionally find per as a radical coupled with ~anto, ~isto, or ~ulo to mean an agent, go-between, or middleman. If you have a good dictionary with notes you may want to look up some of the other things you can do per this super powered word.
That is also true. But you may have confused senpere (without means of) with malpere, a word I've never seen before, and whose meaning I cannot adduce.
Have you been in contact with the Esperanto organization in your country. They should have a reasonable priced dictionary with notes, and commentaries.
Whereabouts do you live? There should be an Esperantist or two living near you. Check with your National organization for details, or go to https://eo.chatterplot.com and see who may be near you. Failing all of that, try making use of Skype and you can literally talk with people all over the world.