I would say in conversation: I’m heading for the railway station. It can of course be used in a figurative sense: That company is heading for disaster/for trouble. ‘Headed’ on its own is of course the past form of ‘head’. My feeling that ‘be headed’ would require an inanimate subject describing in what direction something is going or has been sent as in: The train was headed towards/for the mountains when the accident happened.
Here is my take on your three questions:
1: Both are OK
2: Both are OK
3:
I’m heading to/for the museum –> The verb ‘head’ is intransitive and used in the present continuous tense.
I’m headed to/for the museum. –> In my opinion, the word ‘headed’ is an adjective in this sentence.
The verb ‘head’ (meaning go or move in a certain direction) can be used with quite a number of prepositions and words. Some examples:
head toward(s)
head over to/up to/down to
head out
head home
head back
head north/south/east/west
head in that direction
head your way
‘Head for’ is often used figuratively to talk about a likely negative result or outcome of current actions or activities: He’s heading for trouble./He’s headed for trouble.
The verb ‘head’ can also be used as a transitive verb:
Thank you for your detailed and considerate interpretation, which has drawn me a whole picture for my ‘head’ problem.
Hi Jamie,
Thank you for your precaution, which reminds us of the fact that ‘behead’ will mercilessly put an end to all the activities involving whatever the ‘head’ is.