Is Straightaway One Word?

Immediately. The OED cites a use as early as 1662; the subsequent examples given suggest that in roughly 1900, the predominant form changed from two words (straight away) to one (straightaway), though both versions are still found.

Is it straight away or straightaway?

straight away not straightaway. It's okay to say straightaway in the outside world, but it's not The Writer's way.

What type of word is straightaway?

The definition of straightaway is something immediate or something that extends in a straight line. An example of straightaway used as an adjective is the phrase "straightaway lie" which is a lie told without any hesitation. Straightaway means a straight course or track.