1 Savings accrued before you come to the UK and transferred to the UK won't be taxable in the UK. You need to separate or be able to identify cash and assets you held before you come to the UK so that only any income and gains you make after you arrive in the UK are taxable in the UK if you bring them into the UK and choose to use the remittance basis of assessment.
2 No particular issues arise. See 1 above.
3 Income and gains from Jersey and Isle of Man are treated as offshore income for UK tax purposes as would income and gains from India or other countries.
4 Keep good records. See 1 above on separating or being able to identify capital held before you come to the UK. The identification of income and gains for the purposes of the remittance basis rules are complex.
Take a look at section 9 of RDR1 here for information on the remittance basis of assessment.
I hope this helps but let me know if you have any further questions.
When I say "accrued", I mean, actually sitting in your bank. Realised income would be a better description.
I'm afraid that the record keeping and onus of proof is up to you. If asked by HMRC, you will need to prove that any money you bring into the UK which you claim you had before you arrived was in fact money you had before you arrived. That may mean producing bank statements. I know of people who moved cash held before they came to the UK to a different bank account or put post arrival income in a separate account.
The cash you have outside the UK immediately before your arrival in the UK can be brought into the UK tax free. You could also liquidate assets such as shares and property before you come to the UK free of UK tax (but local taxes may apply).
If for any one tax year, you have non-UK income you have not brought into the UK of £2,000 or more and you wish to use the remittance basis of assessment whereby you only pay UK tax non UK income you bring into the UK you have to make a claim for such treatment. See section 9 of RDR1.
The RB applies to income and capital gains.
Cash held abroad before arrival in the UK can be brought to the UK tax free.
If you own shares or property or other assets which are showing gains and you sell those after you arrive in the UK, the gains will be taxable in the UK if you don't use the remittance basis and instead choose to pay UK tax on your worldwide income.