Q [1]  Please elaborate on question 18 in the following link in your site http://www.english.alhakeem.com/pages/book.php?bcc=147&itg=1&bi=150&s=ct I use cafés to do college work sometimes and it is a public place where anyone is allowed to go on any website except those with pornographic material and so on. What about the library at college?

As long as it is not considered as encouragement to the prohibitions, it is permissible to enter the café and the library and use them.

Q [2]  When it comes to today's way of interacting online, there is something called "smilies" or "emoticons" which show what the person's expression is. Is it permissible for a boy and a girl to communicate through the internet messenger this way?

If the said involves sexual arousal or sexual lust then it is prohibited. Otherwise, it is permissible.