I can see that you have been studying stative verbs (which we don't use in continuous tenses) and dynamic verbs (which we can use in continuous tenses) Stative verbs describe states, while dynamic verbs describe activities. The verb 'think' has two different meanings. Look at these two sentences: 1. I think Italian is a beautiful language. 2. I'm thinking of studying Italian. In the first sentence, 'I think' means 'I believe' or 'In my opinion'. This is a stative use of the verb, and we have to use a simple tense. In the second sentence, 'I'm thinking' describes an activity. It is what you are doing at the moment, so you have to use a continuous tense. By the way, many stative verbs also have dynamic meanings. Compare 'Lemons taste sour' with 'I'm tasting the soup to see if it needs more salt' The first is a fact, so it has to be in a simple tense. The second is an action, so you can use a continuous tense. I hope that helps.

You would use "I am thinking..." in a continuous form to mean that your opinion might change later, or a decision will be made soon. The key is that "I am thinking" is a temporary situation. We are not looking at the length of time.

Yes you can Think : Eg : In a conversation : I think your smart Thinking - usually used when you forget something or you want point to the future There are some other uses as well Eg: I'm thinking to open a shop tomorrow

Your question is confusing. Can you give an example? Are you asking about a construction such as this: "I am thinking about leaving"?