1) Do we pay income taxes in the UK?
If you are residents of UK - yes - your income would be taxable - you will find here some information about UK income tax rates and allowances - http://www.hmrc.gov.uk/rates/it.htm
2) How does FEIE work against the taxes I have paid in the UK and should we apply for the exclusion?
The Foreign Earned Income Exclusion (FEIE) is used on US tax return - it has no affect on your UK taxes. The amount of foreign earned income you can exclude per year is limited by $87,600 ($91400 in 2009) for each person - so together, you can exclude as much as $175,200 for the 2008 tax year. In addition to the foreign earned income exclusion, qualifying individuals may also choose to exclude or deduct from their foreign earned income a foreign housing amount. For 2008, the housing amount limitation is $26,280 for the tax year.
3) Can we continue to claim deductions on our US tax return for mortgage interest payments?
Yes - - assuming you are not filing US tax return as a not-resident alien - you may claim mortgage interest deduction for one primary home and one secondary home.
4) We contribute heavily to charity and will continue to do so from the UK. Can we deduct these contributions from our US tax returns?
You may deduct charitable contributions to qualified organizations in the US that have required registration with the IRS. You will not be able to deduct contributions to UK charities.