1. The work would only be yours by default only if the people who were performing the music were employees (rather than independent contractors) and working within the normal scope of their employment. I believe that usually, session musicians are considered independent contractors, so without a signed written contract, the copyright to their performance would be owned by the musicians (and possibly the editors, sound engineers, and so on) (see 17 USC § 101 for "work for hire" definitions). I believe many of the musicians' organizations which assist in contracting out session musicians also have work for hire/copyright assignment agreements they like to use.
So bottom line is this: Without a signed contract specifying that all rights to the recordings belong to you and signed by anyone involved in production, you may not own the copyright.
As for whether or not the performers could stop you from distributing the work: No, probably not. You would own the copyright (assuming you have your signed agreements in hand) and would be able to distribute the work as you please. 17 USC § 106A does contain some rights similar to those at-hand in your inquiry, but § 106A applies only to visual art, not audio recordings.
2. The performers or their employer would hold the copyright to the recordings of the performance, and it's likely that they're just sending along the contract in order to reiterate the actual state of the law (as well as possibly to add a layer of contract over the copyright they already own). You cannot make copies, broadcast the recording, or otherwise use it in violation of the copyright law.
Of course, if the recording was made without your permission, you might have an argument that 17 USC § 103(a) renders that work unprotected by copyright, since § 103 states: "protection for a work employing preexisting material in which copyright subsists does not extend to any part of the work in which such material has been used unlawfully". At the same time, if you (or anyone acting under your authority) have recorded and distributed recordings of your work to the public, subsequent recorders of the material may be entitled to a statutory license under the terms of 17 § 115(a).
I'm guessing that, since this was a competition in which the winning work was to be performed and recorded, the entry form probably contained some language licensing the work to the promoters of the contest in some way, so I doubt that the above paragraph would really apply, and it's just included for completeness.
So bottom line again: You don't own the copyright to the performance, and if you do anything which violated the copyrights of the person owning the right to the performance, you may be liable for copyright infringement.