Employment contracts and long periods of silence

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Hi /adv/, sorry for the long post. I've signed on to work with a great company but since it's my first 'real' job, I'm nervous and want some second opinions.

As part of my degree I need to complete a few months worth of work experience, which I was initially going to do on site with my employer. Since then I've received an offer for 14 weeks work with the faculty at my university. I'll be paid $3000~ to do something I'm well suited to. The problem is that the contract I signed in June has a conflict of interest clause that forbids me from working with
"any company, industry, entity, which is competitive to any of the business conducted by us ;any other employment that could adversely affect your performance."

While there's no competition between the two entities, both jobs utilize the same very specific set of skills. I imagine this is only positive as it allows me to develop, something no employer could object to. However, I'm still nervous. Is it worth asking my manager about or should I just go ahead with it since it will finish before my main job begins?

Also, what level of contact should I be in with my employer? Is it normal/common for employers to offer contracts of employment 6-10 months before starting the job, then have minimal contact until the day it begins? I feel like I should email and schedule a meeting to touch base and talk about what training I should be doing before starting.