Discuss and learn French: French vocabulary, French grammar, French culture etc.
In (1), just be careful at the end: after "à", you need the infinitive: difficile à croire. You could also say Je le trouve difficile à croire. In everyday speech, people would probably just say Ça m'étonnerait.
In (2), depending on exactly the context you can translate this pretty much literally: Tu as été très occupé récemment?, or e.g. Tu as eu beaucoup de travail récemment?
In (3) I would recommend simplifying slightly and saying e.g. On ne s'attendait pas à ça or (a bit more informally) Ce n'était pas prévu, ça.
Again in (4), the key is to simplify. If you're expecting somebody to come, you're effectively waiting for them. So just say Vous attendez quelqu'un aujourd'hui? For emphasis, e.g. if you want to express the idea that "aujourd'hui" is unlikely/surprising, then a more literal translation would be Vous vous attendez à ce que quelqu'un vienne aujourd'hui?, or you could say e.g. Vous pensez vraiment que quelqu'un va venir aujourd'hui?
Some of these answers mix some slightly more advanced grammar points, so you may wish to come back with questions about these suggestions...
P.S. For (3), a slightly more formal and closer version could be On n'avait pas prévu cette éventualité.
Je dois vous remerci de m'aider. My level of french is not that good yet so I have some difficulties trying to remember some of the phrases. I think this is because if one is not fluent enough yet some of the words are difficult to remember. It will take quite a while to overcome this problem and only after making effort to read a lot will solve this problem. I don't encounter this problem in english anymore because I read so much in english. I am not loving forward to reading a lot in french because it is time consuming that's the problem. Once again thank Neil, very kind of you to help with the translation.
mistake in 'I am not loving forward to reading' it should read ' I am not looking forward .....'