Applying for new H1B after 6 years with CAP

[Jai13092016]

Hello,

I am a H1B holder with ~3months left on it. Due to some unforeseen personal reasons I could not apply for a green card in time.
I am staying in India for one year so that I can apply for a new H1B.

Questions:
1. My stay abroad for one year ends on 7th May, 2018. Can I still apply for a new H1B in April 2018, as the applications are sent soon?
2. How long before I find out if I have been picked up in the lottery process?
3. If I do get picked up in lottery and I am approved, when will be the latest that I will get to start working on my new H1B? Will it be in October 2018? 
4. Is it possible to apply for premium processing? 

All this is new to me as I originally went on an L1 visa and H1B is new to me. 
I am quite worried at this point and would really appreciate any input and help from you all.

Thank you,
Raju

[Jai13092016]

Please consider this while answering the above question, I just realized I should have mentioned some more information:

I left USA in November 2016, but I went back for about 5 weeks on a B1 visa as I had to close my home, car etc. So, if I calculate one year it would be 365 days + 5 weeks that I should stay out for me to be eligible for a new H1B?