Paying interest on a mortgage on your residence allows you to deduct the interest, but only if all of your itemized deductions (mortgage interest, charitable donations, qualified medical expenses) are more that the standard deduction. So it only "lowers your taxes" to the extent that it gives you a bigger deduction.
Property tax is deductible as well, but also would only help you if the total deductions are more that the standard deduction for you or your family.
And yes, it applies to a mortgage on a mobile home (or condo, but not rent on an apartment since you don't "own" it). It does not apply to properties you own but do not live in (e.g. rentals)
Would I be able to write-off repairs on this mobile home?