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Good afternoon, once you have been in the U.K. on under the 10 year route after a year you can apply for British citizenship then your British passport.
Yes the 3 years on student visa would be considered in the 10 year period.
That is correct after student visa if you obtain a work visa this will get you to 10 years then once have permanent residence you can apply for British passport.
If you are in employment you can change employers if they are willing to take you on.
It was a pleasure assisting you today. Take care