Taken or being taken?? I am very confused!

a little bit background: I am a non-native English speaker and I am a teacher in an area where the students are not too good at English and the idea has to be expressed as simple and clear as possible. However, I am very confused with participles.

So, I would like to know if there are any difference between these two:

Being hit by the lorry, she died.
Hit by the lorry, she died.

Any difference between this two sentences? anything wrong????

How about these two?

Late for school, he was punished by the teacher.
Being late for school, he was punished by the teacher.

Thanks!