H1-B cap exemption rules?

I was on an H1-B ( 3years/6) No PERM filing
I have been working in London for 1.5 years now (Tier 2 work visa)

If I were to get hired by another US firm today, I believe they can file an H1-B cap exempt petition since I have 3 years left on my H1-B

(Currently no plans as such to move)

My current employer wants me to fly for a work trip to the US on B1/2 visa for 2 weeks.

Will getting a B1/2 visa potentially eliminate the H1-B cap exemption from another employer? I.e. will it limit my potential future employment?

What if I go after I get the UK passport in 4.5 years time? Will using ESTA impact the H1-B on my Indian passport?

Yes, that is correct.

No. B1/B2 do not impact your eligibility for cap-exempt H1B for remaining term of 6 years.

Your H1B visa stamped on your Indian passport should have anyways expired already. Traveling on ESTA using British passport will not impact your cap-exempt eligibility.

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Thank you so much for your response!