1,You are right,application of EAD won't harm your H1B
status.
2,Check on www.uscis.gov/case status & processing date
/Texas Service Center/I-765
3,you should fill it as a fact & explain it's OPT
status.
2,Check on www.uscis.gov/case status & processing date
/Texas Service Center/I-765
3,you should fill it as a fact & explain it's OPT