I've been reading a lot of graded readers lately (targetted at JLPT N4/N3 level). I recognize that these are not "pure authentic native Japanese", but I also don't believe they are ungrammatical.
One thing that has been very conspicuous is the use of verbs of movement (eg 歩く、走る、etc) in compounds with 行く and 来る. In fact, this almost seems more common than using the verb by itself. As an example, a sentence might read
Is there a major difference in meaning or usage between 歩いて行く and 歩く? Is there a stylistic difference between the two? Which would be most common in day-to-day conversations?