Translation:Ik geloof dat alles met communicatie begint.
True, but in these kind of sentences geloof is used in a broader sense in Dutch, not just religious or something that cannot be checked, but also things like: Ik geloof dat je je linkerschoen aan je rechtervoet hebt aangedaan. = I think you put your left shoe on your right foot. Which clearly is something that can easily be checked, so I don't think believing is used in English in these kind of sentences.
Yes, I understand. Afrikaans is exactly the same. "Ek glo..." or "Ek dink..." = "I believe..." in certain circumstances.
Believe is absolutely fine in that sort of sentence, it would just be a more disparaging way of saying it [in my opinion]. In your example; 'I believe you have put your left shoe on your right foot' might be used by a less likeable person while they are disagreeing with you in order to discredit you by making you look dumb. That sounds like a very childish example though.
People will interject mid-conversation to correct a fact all the time with "Actually, I believe that is...". They just tend not to be very likeable people.
I lost track of why it felt so important to type this out mid paragraph. Sorry...
You can, but the meaning is a little bit different. When you use 'denk', you imply that you are not sure, doubt. If 'geloof' is used, you'd imply that even though you cannot prove you are right, you believe it is. :)