1a. She has begun to learn/ learning English since 2003. (wrong)
You have marked the above sentence as wrong.
1b. She has been beginning to learn/ learning English since 2003.
2a. We have come to this beach since 2012.
2b. We have been coming to this beach since 2012.
3a. She has learnt English since 2003.
3b. She has been learning English since 2003.
What about the other sentences?
Please explain the nuance of the grammar involved with details.
Thanks.
1b. She has been learning English since 2003. 'Beginning to learn cannot be right - she can’t still be a total beginner if she’s been learning for 12 years.
The other sentences are okay.