H4 expired, L1 rejected, applying for H4 again

Case :

I was on H4 visa valid till June 2015. My husband has got his H1B extended in US, however it could not be done for me as I came to India in Mar2015 and have been in India since then. I went to US on a sabbatical for 6 months from my employer. In Jul2015, I applied for L1B Blanket visa with my employer but it was rejected.

I had also applied for admission at a university and they have issued me an I-20 in may2015 for obtaining F1 visa at the US Consolate in India.

Now I am planning to apply again for H4 visa.

Questions:

Does the issuance of I-20 affect my H4 visa processing? should I get it cancelled?

Does the rejection of L1-B Blanket visa have any affect on H4 visa application?

I dont think rejection of L1B would affect your H4 application. But be clear while filling ds160 with all the relevant information. Dont try to give any false information as definitely it would affect. Probably the I-20 might affect partially in case you go for visa stamping only in such a way that interviewer might ask some sort of questions. Because with in short span you have tried with multiple options to get into US. But chances for tough interview is 5-10% only. These days depending on the criteria, they are asking for drop off option in case if you need to attend visa interview as earlier also you are on H4 and again you are planning for H4. so here chances are about 5% only. so at bottom line i would say it might not gonna affect you at all. be bold and clear to mention about the details without fail.

Thanks chak132. Will the embassy have knowledge of I-20 as it was issued by the university? If I get it cancelled now, will it mitigate all chances of risk in obtaining H-4?
I checked and I am not eligible for the dropbox option as I have had a visa rejection in between.