Translation:She prefers writing on paper to writing on a computer.
In English, both to write or writing are acceptable answers here. The preferred and more natural way would be "she prefers writing on paper" rather than "she prefers to write on paper". I know in romance languages, you can only use the infinitive form, but in english, the gerund is acceptable in this context (and preferred, like I said).
Yes, "via" can be "by means of", but remember that in English, certain words are only used in certain contexts.
You could say you communicate with someone via computer, or more likely via Skype or via email, and you could potentially write someone via computer too, even though that it is starting to sound strange, but you would be writing on a computer, not via it. Via implies some form of transit.
If you say you "write via computer", you are not intending for the writing to stay on the computer itself, but it is going somewhere else, and whatever you write is just passing through the computer on the way.