I could not use up my 6-year H1B period fully. Can I file for an H1-B transfer and avail the remaining period (2 years) or Should I file for a new H1-B? Can I attend a conference in US with a visitor’s visa?

You could certainly file to exhaust your initial 6-year period. You will not be subject to the CAP. Alternatively, you could seek to qualify for the H-1B CAP beginning October 1st (fresh six year period). You could apply for a visitor’s visa independently.