No, it won't. When you order your own credit report, be it during your trial membership or at any other time, it's called a "soft inquiry". Soft inquiries do not impact your credit score, and don't appear on your credit report when a lender views it.
A "hard inquiry" is placed on your credit report when a company reviews your credit as part of an application. Having too many hard inquiries could mean that you are overextending yourself and could potentially lower your score.
Yes, the process of sending and receiving your information is encrypted using Secure Socket Layer (SSL) encryption. This technology helps ensure that your credit card and other sensitive information are protected. Preferred web browsers are Internet Explorer 6.0+, Firefox 2.0+, and Safari 3.0+.