I wouldn't worry. From your recounting the facts it seems that you were in valid status at all times.
In any event, your last entry and lawful admission on H-1B status "cured" any periods of "unlawful presence" or lapses you might have had. I believe you've had none since you started working fr the petitioning employer as soon as the H-1b was approved.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
If you were granted a change of status and did not overstay, then you were not out of status.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
Hard to say without seeing the documentation. It appears that your employer did not request a change of status if you received an H-1B approval without a replacement I-94. This would mean that you did not maintain your status. On the other hand, you were granted an H-1B visa and allowed to reenter. You are now in status but may have been out of status during your prior stay. However, your admission as a student prevented you from accruing unlawful presence.