Can you get an honorable discharge under chapter 5-17 with a recent article 15?

The answer is yes,
AR 635-200 states
"5–1. Characterization of service or description of separation
a. Unless the reason for separation requires a specific characterization, a Soldier being separated for the convenience of the Government will be awarded a character of service of honorable, under honorable conditions, or an uncharacterized description of service if in entry-level status. "

So under this separation type, the commanders choices are honorable, under honorable conditions.

An article 15 isn't going to have that much of an adverse effect on your career; however, other events in your career [ie, attitude, adaptability, following orders, etc] can result in "other than honorable" discharge. To answer your other statement, if you need medical assistance get it!!! The correct diagnosis can change your career and life for ever.

Yes but it is usually reserved for the first GO in the chain of command.