Does anyone know of a way that I can search for Diablo 3 profiles by name and view them? I mean looking at character, items, played time, etc.
I couldn't find such functionality on battle.net.
If you know the exact battletag you can visit the official site: http://battle.net/d3/
There you will find a nice diablo oriented display of all the important and more or less unimportant stats including but not limited to:
However if you don't know the exact battletag you can visit the semi official site http://www.diabloprogress.com/
Here you can just look for the player name whithout the #numberhere. The original purpose of this site is displaying a ranking based on different aspects of the game so it's not as well designed as the official D3 Website but has a clean structure for the competitve aspect of the game.
Basically what you should do if you just want to look at someones profile is:
Go to the DProgress and search for the Battletag name of the users battletag (you can't search for the character and there is no site where you can do that) and you will either be instantly redirected to the right user or you recieve a list of users with a similar name.
Example of finding out a complete battletag via DProgress: If you type in my username "Jutschge" you will see my character sheet of DProgress with the battletag. However if you type in "Killer" you will see many different users with the Battletag (Killer#1234, Killer#2341 etc.). You have to know some things about the person you're looking for and the best thing would be a character name so you can filter the results of your search based on characters.
Now If you have the complete battletag you can go back to the official site and search for it there or you can click the "battle.net" link that's onthe DProgress site itself. I would recommend using the official site if you aren't interested in competitive rankings because DProgress isn't always up to date.
You can use the search field at the top right on the official site:
What you need to do is search for the complete battletag there, i.e. Proplayer#1872. This will let you look at their characters and items.
If you want to search by player's name only use google
letstrade diablo 3 profile
but only if the users have posted some stuff in forums