No, but you can claim interest and repair costs as a means of lowering your income and other taxes. Taken to an extreme there are some people who pay net zero tax on millions in net income (they don't mind the loss as there is no tax and the long term plan is to make a capital gain on sale).

The original idea was that people would lower the rent to make renting more affordable. This rarely ever happens in practice because tweaks to the law mean that you can claim interest and expenses without actually renting the property (set the rental at an unaffordable price point and leave the house vacant).

Which has the added benefit of reducing supply, driving up prices and raising the future resale value!

No, you can't deduct capital expenses like a renovation from your personal income, but you can deduct those capital expenses from the eventual capital gain so that the capital gains tax is only paid on the net profit.

The negative gearing only applies to ongoing expenses (e.g. maintenance, interest, depreciation) not to capital expenses.