Is it right for me?

Yes, I think Drupal 7 would work for your needs fairly easily, mainly using Drupal Core; the 'contrib' modules add flexibility to your task -- if you find you need a specialized function that doesn't seem to be in Drupal, chances are very good someone else has already written a module to do it. Come back to this forum when you find yourself wondering "What module does function X?" and someone here can almost certainly point you in the general direction.

Beyound that, a couple of comments about specific needs you mentioned above:
a) CMS to hold several of the same type of page, so it should preferably be able to have a page template that can be reused. . Drupal 7 can be that CMS; there is a built in content type called 'Article' in Drupal 7 Core which will help you build, maintain and edit the given "page"; all this is stored in a MySQL database out of the way, so all Drupal has to do is bring up the appropriate "page".
b) Each page should have an application name, uploaded document files related to it, the servers in which these apps are running on, and support contacts related to that application (especially the contacts should be stored in a database since we reuse many of them and bind them to different of this application pages). This particular requirement I don't quite understand, so if I say anything wrong in here, I hope other more experienced users will recognize what you need & direct you accordingly. My only observation from the terminology you use, is that it seems like you are thinking about building a 'mobile' site. A number of Drupal's themes ('skins' that help produce a particular "look and feel") will help you support mobile as well as laptop sites, right out of the box
c) the search results need to display particular fields of those pages, being able to search by server/system, contacts, applications. (Preferable, not necessary). The custom search that comes with Drupal Core is pretty powerful, and should allow you to do most of what you want here. if that is not sufficient, there are contrib search modules such as Solr Search can provide more
d) ...edit each page and the related information directly on that page or link to the edit page from there, instead of using an admin panel (Only for these pages, templates and any other admin information can use an admin page).. I would not recommend this approach from a security standpoint (you would probably end up with millions -- literally -- of "Viagra articles" on your site using this approach (my experience). That said, install IMCE editor and WYSIWYG and you will have 1) a very capable editor; and, 2) control over who can make changes to content on your site (which can be to almost anyone you deem appropriate for the role (including admin). While the easiest way is just to make it so "you have to be admin to edit the page", you can delegate this duty to some person or group responsible for site maintenance/upgrade.

In the long run your questions are more likely to be "How do I do that in Drupal 7" rather than "Can it be done with Drupal 7": I'll recommend a few resources I've found very useful in my Drupal 'career':
a)Beginning Drupal 7 -- just reading a couple of the beginning chapters will really open your eyes to the posssibilities Drupal offers.
b) Almost any of NodeOne/Johan Falk's excellent Drupal videos -- these will help you come up to speed fast.

Good luck & have fun playing with your new Drupal site,

Jeff Nutting

Yep you can do this with drupal fairly simply-- i did this very type of site.

Create content types for each type of item (server, application, vendor, etc). Contacts can either be actual users (if they will be users of the system) or another content type. You would use the entityreference field to relate them to each other and the views module to create searchable listings (using exposed filters).