Hi. The first phrase may make sense depending on the context:
"hasta el otro año entro"
It may be: "hasta el otro año entro... a la escuela" which means "I'll start to go to school "until" the next year"
The second phrase, in my opinion is actually right, in the sense that people may understand you, perhaps is not the perfect grammatical way to say it, but it makes sense to me.
"hasta ahora que veo tu mensaje" or "hasta ahora veo tu mensaje" may be translated as "I didn't see your message until now" however, a better way to say it would be "no vi tu mensaje hasta ahora". That way it even resembles more the English version.
Remember, people don't speak perfectly in daily conversation, so it's useful to learn this sort of expressions too.
The word "HASTA" may has different uses in Spanish that the word "UNTIL" in English does not. They already wrote some examples in the answers. Here are some more:
-Él comió muchas cosas, *hasta* se comió una rana.
He ate a lot of things, he *even* ate a frog.
-El hombre *llegó hasta* la luna
Man *reached* the moon
-¡*Hasta* que te encuentro!
I *finally* found you!
-¿Debemos ir *hasta* allá?
Do we have to go *all the way* there?