There's nothing at all wrong with the "I want to make sure that" part of your sentence; the part that I find a bit obnoxious from a politeness aspect is the passive construction "it would be appreciated." You'd be much better off expressing your appreciation directly rather than simply allowing for the possibility that some unknown object somewhere will be gratified:
Further, I'd like to make sure that the dates of the courses will not conflict with my other appointments, so I'd be grateful if you could supply more details about the arrangements and what their costs would be.
(There are also a few other minor things that I've tweaked, particularly the placement of "that" in the first phrase, and the use of the singular pronoun "it" to refer back to the plural "arrangements".)
There's a bit of a disconnect in that you've specified that you care only about the dates but then you go on to explicitly request cost information as well; but if you've mentioned the cost aspect prior to this sentence, it's not a problem.
In general, it is more polite to ask for help achieving "something" than to ask directly for the "something".
I would like to ask you if it is possible to secure me an internship with a software company.
could be rephrased as
Would you be able to help me secure an internship with a software company?
First, we turn our thought into a question so that it seems less like a demand, and then we ask if it is possible that she might be able to help. This way even if she can't directly find you a position, she may still be able to help by introducing you to someone who can.
I would also rephrase the second and third sentences:
I will have approximately two weeks free between first and second semester, and I would like to use that time to increase my experience.
This isn't English advice, but I can't help but add that in my experience in the US, two weeks is a very short time for an internship. Instead of asking for help getting an internship, you may want to ask for her advice on how to get practical experience during that time.
I was a part time intern for a professor in the Engineering school while I was pursuing my degree, and it worked out well because my work was close to my classes and the university had a process in place for hiring students. A position with an outside company is more difficult to secure because there is a lot more cost in hiring a new intern and they will likely want a longer commitment.
Best Answer
At an interview, you should not be too effusive with your greeting, or too verbose (unless invited by a leading question intended to draw you out). The interview panel makes the moves, so I suggest you be polite and uncontroversial.
is sufficient, with a brief look around the interviewers to make it clear you are greeting them all, and wait for them to take the lead.