Is iCloud is not backing up my iPhone completely? My iCloud is not backing up my device (iPhone 4 with iOS 5.0.0) completely.

When I try to backup my Contact List or Mails via iCloud; It only backups the newest added contacts or recent mails. (Beginning from last restore) For example. I have 220 contacts, I added 10 more after updating to iOS 5 (fresh restore) When I run iCloud. It only backups the 10 contacts. 

Is this how it is supposed to work?
Here a link to a Macworld article that contains a terrific explanation of how iCloud backups work. The answer to your question is that iCloud performs incremental backups--only what has changed since the last backup will be sent to iCloud on the following backup. 

This means that, for example, if the initial iCloud backup contained 2.0 GB of data and then only 0.1 GB of data changed (say, Address Book contacts), then only those 0.1 GB will be sent to iCloud. This saves battery and avoids transferring data that iCloud already knows about. This is the same principle behind Time Machine on the Mac. 

(There are other nice things that iCloud does for the sake of efficiency. For instance, your iTunes purchases are not sent to the iCloud backup, only their references, since Apple already has the songs themselves in iTunes)

In general, I would say that if you backup regularly, then each subsequent backup should stay relatively small and should complete in a short time. The exception is, naturally, when you have recently added large amounts of media like photographs or video taken from the Camera app. 

I recommend giving that article a read. It is very comprehensive. Hope this helps.