They have no obligation to email you, call you, interview you, consider your feelings, respect your time, or acknowledge you in any way. These things happen, for a variety of reasons.
Let it go. This isn't a battle that needs to be fought.
No, you should not file a complaint against her. However, you should mention to her, calmly, that you did email her, repeatedly, to follow up about this job, and received no response, and that she should check her spam filters and/or trash bin to see if your messages got filtered. Spam filters work weirdly and are not always correct, and weird things ...
Taking out the emotions from the situation, which includes your opinion on his effort levels, does he meet the minimum expected standard that is required to do the job to the expectations of the customer/bosses? If yes, this is solely a personal issue. If not, you need to highlight this objectively with factual information.
What you should do depends on you, but let me tell my thoughts which are quite a constrast to the first answer that was given.
Your apprentice payment can't be compared to normal salary at all. This seems to change for you in a few weeks.
If you really like your current job with all that is around and it's only about payment, isn't it the worst moment to ...
I suppose you can try to encourage the intern to think, learn, and work more independently.
For example, when the intern asks for help, you can:
Ask him what he has done so far to try to solve the problems
Give him some good suggestions on how to solve the problems
Encourage him to try out the solutions on his own based on your suggestions
Make it clear to ...
When you talk to your boss, point out that you know you are short-staffed, and this intern is helping to the best of his ability, but his ability doesn't include any independence or figuring things out on his own, which is taking time from you.
So you are actually more short-handed because of him, and while the internship is helping him, it should not be a ...