Luteal Phase: Clomid/Progesterone

Hi - I have had 2 chemical pregnancies in the last 3 months. I just went to an RE and they said I have a Luteal phase defect. I ovulate on day 20 or 21 and have a 10 - 11 day luteal phase. He gave me a prescription for Progesterone and also mentioned Clomid. If you have experience with this, I wonder if you could help me understand the questions below...thanks so much. Of course, all of the questions came to mind after I left the office.

1. Does progesterone actually increase the length of the luteal phase? I know it increases the uterus lining to prepare for the baby.

2. I know Clomid helps to ovulate earlier, but does it help with a short luteal phase? Since luteal phases usually do not change, if I ovulate earlier with Clomid, would my luteal phase stay the same?

3. Does Luteal Phase Defect just have to do with the length of the luteal phase or would you say late ovulation is also considered part of the LPD?

4. Is egg quality or uterus lining "too old" with late ovulation? Why would late ovulation be bad if the luteal phase was sufficient? For example, if I ovulate on day 23, but my cycle is 37 days. The luteal phase is still 14 days.

Thanks for your feedback.