N-Grams - how to predict further into the future and how far can we predict?
There's no simple answer to "how far into the future can you predict?".  Obviously, the further you go, the less your ability to predict.  For English text, I would expect that ability to predict would decrease rapidly.

You asked if there's a better wya to do this.  You can of course consider a generalization of $n$-grams where you use the characters at positions $i-n+1,i-n+2,\dots,i-1,i$ to predict the character at position $i+k$ (instead of predicting the character at position $i+1$), for any fixed $k$.  This will probably perform worse the larger $k$ is.

You might also be interested in skipgrams.