I am a Japanese learner and I would like to know if my katakana handwriting is readable.
Your writing is generally readable, but here are some advice:
Katakana is meant to be composed of straight strokes. The subtle curves you may see in typefaces are reproduction of "human" trait that we inevitably involve roundness when we try to draw straight lines, and not that you should trace it, especially in handwriting.
This font is very close to the bare structure what we "intent" to write, though there is little chance the actual outcome would be like this unless you put really strong force on the pen.
Your characters look as if "italicized". While they come to more or less oblique in fast horizontal handwriting, deviation from upright posture is not considered normal because of handwriting (remember, Japanese is also written vertically). Try make vertical lines exact perpendicular, and left- and right-ward strokes symmetric angles in ハ or メ. Moreover, rightward strokes in ソ (so) and ツ (tsu) should be rightward at any rate.
ク (ku) should be written like its original kanji 久 without the last stroke (i.e. a bit oblong), while a good practice of writing ワ (wa) is thinking it of a broken downward triangle (▽).
As already commented, ム should be written in two strokes whatever the previous character is displayed like in your environment, unless you're the sort of person who writes "a" in two stories :)