Hi dipjyoti,
I think you have no problem.
1. F1 visa is not an immigrant visa. So, People with J1 HRR is eligible for F1 visa. My F1 visa advisor told me so. You even don't need to get a waiver.
2. Your stay under J1 will be only summer. You have a big chance to get a waiver if you apply for. My visa advisor told me that the J1 host institute is more likely to give away no objection letter for a short time J1 person, such as 3 months program. You may contact to the officer of the summer program about this and explain your concern. You may simply want to get a waiver for your future (after F1). To apply for J1 HRR waiver, you may need the reason to apply (J1 HRR is bothering you). Since J1 HRR will not bother your F1 visa acquisition, you may have no reason to apply for a waiver yet.
3. You will complete your J1 HRR by the time you finish your graduate school. You will be in your country for a year after the summer program. This will be counted as 1 year for your J1 HRR. Then you go to US for your graduate study under F1. You will go back to you country for summer vacation, a semester for data collection, a semester for intership, or two 2 semesters for writing up thesis. These are all counted for your J1 HRR. The home country residensy after J1 (even you are on F1) will be counted for HRR.
I got these information last year. There maybe some changes or I might have misunderstood some parts. I recommend you to check the information with your summer program officer.