Is the annual property tax payable from pre-tax income (as in the US) or from post-tax income (as for the UK council tax). Stated in a slightly different way, is property tax income tax deductible?

Payable from post-tax income and generally not tax-deductible, the same as mortgage interest.

U can only deduct it if you are running a home based business / or use part of your home to generate an income and then you are only allowed the deduction based on the proportion of the home used...AFAIK

You cannot deduct property tax (or mortgage interest) on your home. However, if the property produces taxable income (e.g. you have a tenant, or a home based business) you can deduct part of these costs.

If you use the home business deductions, and then sell the house for a profit, do they still tax the capital gains in proportion to the amount claimed for business deductions, there by making in totally pointless to have claimed the deduction in the first place?

Same as the UK then, thanks.

In theory, each time you change the use of your house there is a deemed disposition and acquisition that could trigger a capital gain.

Say you have a 2,000 sf house - 1,000 up and 1,000 down that is worth $300,000. In 2010 you decide to use the lower floor for business. At this point there is a deemed disposition and acquisition. The lower floor now has a tax cost of $150,000 (300,000 x 1,000/2,000). Regardless of what you paid for it there is no tax payable if the whole house was your principal residence up to 2010.

After 5 years you need to move the business to bigger premises. The house is now worth $425,000. If you keep the house and convert the lower floor back to personal use there is another deemed disposition and acquisition. You have a capital gain of $62,500 ((425,000-300,000) x 1,000/2,000). $31,250 taxable. There is no capital gain for the upper floor as it has continued as your principal residence throughout. The same calculation is made if you sell the whole house.

That is the theory. In practice, the CRA do not assess a capital gain if the business use of the house was/is incidental to its use as a principal residence. While there is no clear definition of incidental it is generally taken to mean does the taxpayer claim capital cost allowances (CCA - depreciation for tax purposes) on the house? If they do claim CCA the business/rental use is not incidental, if they do not claim CCA the business use is incidental and therefore a capital gain is not taxed.