OK, a number of points here.
Yes, of course you can transfer the ownership of the property to your partner - you'd have to do that at the LR because it's the income deriving from the asset (house) that you want to align to your partner. Not sure the level of transfer cost it gives you the LR though.
Its the NET income from the property that counts for tax - the gross income less all maintenance / renewal costs including mortgage interest.
There may be a cunning way to do this - but you'd perhaps have to ask for tax advice (because I can't advise you): if you paid your partner a believable sum of money per annum for running the property for you (£3k, say?), it might do the trick. Wouldn't create NI liability at that level - but she'd obviously have to declare the £3k as income to HMRC.
Yes, you only pay 40% on the minimal amount that goes above the 20% threshold upper limit.
Yes, pension contributions you make are deducted from your income (by your employer) before calculation of the net salary (on which your income tax is assessed).