Do you believe in your dreams
No.
There is nothing to "Believe In"
Dreams are fragments of memory that is stitched together by our minds while sorting and filing.
Like a whole bunch of papers scattered on the floor that need to be put away in the cabinet. Pick up one paper, associate it with a known other paper and put it next to that one. As we sort the stack new associations are formed for reference. Those associations work together to allow us to access memory.
Think of Rapid Eye Movement as a scanning system where you scan multiple memories in different places in your mind and place them in an order.
I dream every night.
You dream multiple times. Think of it as putting data into folders that are put in folders that are put in folders. REM is gathering and Deep Sleep is actually setting the files in place where they belong. Time is irrelevant during REM. You might 'feel' like you dreamed all night but you really didn't.
I have had a strange dream
When compared to sentient thought all dreams are strange. Conscious thought has a flow pattern to it where dreams have no flow pattern except what your sub-conscious builds. Since it builds patterns from fragments and fills in gaps for association they seem to have a semblance of order. Its like looking at a picture with parts missing. You fill in the gaps to make sense of the picture.
Does this sounds crazy to you ?
No.
People will always find associations in their dreams. We associate many memories with emotions. Sanity is established by society. We are social animals. Sanity changes as society changes. Dreams are not social they are individual. Thus sanity cannot be established. You are neither crazy or sane when you consider your own dreams.