The beliefs around the origins of Friday the 13th can vary, depending who you consult. But to make a long story short, it's a combination of two different threads of superstition coming together.

The first being that Friday's are unlucky, and the second being that the number 13 is unlucky, making the belief that when these two unlucky elements come together they create a very unlucky day.

Chaucer alluded to Friday as a day on which bad things seemed to happen in the Canterbury Tales as far back as the late 14th century ("And on a Friday fell all this mischance"), but references to Friday as a day connected with ill luck generally start to show up in Western literature around the century.

"It was accounted unlucky for a child to be born on a Friday, unless it happened to be Good Friday, when the event was counterbalanced by the sanctity of the day."   (1870)

As for the number 13, the most common supposition is the superstition is based on the Last Supper in Christianity, where there were 13 dining. Since many of the references to 13 as unlucky seem to be around meals and groups, such as if there are 13 people seated together for a meal it foretells that one will die.

Is there any seeming accuracy to these superstitions and the superstition of Friday the 13th itself, is the day 'unlucky'?

Not that I could find.

From personal experience, 13 has been a lucky number for me. Friday's have generally been good days... and I've no memory of an unlucky Friday 13th.