L1 + H1 Eligibility after 365 days cooling period

USA H1B Visa
1

Hi

I was in USA from 2014 July 25th to 2018 Nov 8th with L1B and 2019 Jan19th to 2020 September 19th on H1B visa. I am currently in India. Here are my questions

  1. Am I eligible to travel back to USA with Existing H1B (since I have not used all 6 years in H1B) after 20th September 2021?

  2. Am I eligible to apply Fresh H1B lottery in 2021(my company already submitted my Visa, not sure about lottery yet) and travel in early 2022?

  3. Please suggest alternate solutions to go to USA