"Think of" usually means "bring to mind".
"I just thought of something!" (Something just popped into my mind.)
"I'm thinking of the time when we went to the beach." (I'm bringing it to mind.)
"Think about" means to go over it in your mind.
"I'm thinking about going to the movies tomorrow." (I'm going over in my mind whether or not I should.)
"I'm thinking about the time when we went to the beach." (I'm going through the memory.)
As we can see from my examples, sometimes they are exchangeable.
"Especial" is wrong, it's only ever "special". In terms of the adverb, "especially" is used to mean "very" or "extremely", or "particularly". Both "especially" and "specially" can mean "for a special purpose", and only "specially" means "in a special manner".
"That food was especially good." (Very/extremely)
"I like all of them, but especially him." (Particularly)
"It was made especially/specially for her." (For a special purpose)
"She was treated specially on her birthday." (In a special manner)