My British pension is showing up in income summary as net employment earnings. How can I fix this?

It should be entered as 'Other Pension Income" under the Foreign Income entry.

Can I include a British pension when calculating the split-pension amount?

Pension from any foreign source pension income that is tax-free in Canada because of a tax treaty that entitles you to claim a deduction at line 25600 is not eligible for pension income splitting. There is a tax treaty between Canada and The United Kingdom of Britain.