Yes, "to learn" can be translated in these ways. We also sometimes translate it like "to study" for "learning language(s)". One more thing, depending on the situation,, present tense is used for future in Japanese.
When we hear 私は毎日日本語を学習します and 私は毎日日本語を学びます, they imagine us that you haven't started yet. If you already started, I would say:
私は毎日日本語を学んでいます or 勉強しています。
I hope this was helpful.