Is the price written on Apple website including taxes?

If you are placing an order from the Apple.com website in your country, towards the end of the order process before your submit your payment information it will show you the final amount with all state/local sales taxes added. You can go through the process but not complete it (if you're not ready or certain you want to buy) to get an exact total.

In the US, no. Sales taxes vary from state to state and sometimes from City to City and are not included in published retail prices.

That would depend on the region.