To add to what toby has already posted:
I am a PR in Canada.
1) Are there any taxes if I inherit some money or real estate from my parents currently who currently live (thanks God) abroad? In my previous country there is an Inheritance tax.
No. It is taxed in the country where your parents live. Once the foreign inheritance tax is paid the net proceeds are not taxed again in Canada.
2) They helped me buy a house on mortgage here by giving away some money to me for the down-payment. Do I need to pay tax here for this amount?
No.
3) If so, will it help from taxation point of view to show it as a lending from them that I will pay back after some time.
As long as your parents are not registered as part owners of the property it is a non-issue.
4) How does inheritance work in Canada? Is there a online reference that I could read?
There is no inheritance tax in Canada. When you die all your capital assets are deemed to have been sold at fair market value on that day. Any capital gain that has accrued in your lifetime is consequently taxed on your final tax return. There are some exceptions, notably your principal residence and anything you will to your spouse. As toby also mentioned, life assurance policies that designate someone other than yourself as the beneficiary are not considered as your capital property and the proceeds are not taxable.
It is a bit more complicted than this in some cases and, in my self-serving opinion, often worth getting the help of an accountant if the deceased affairs are anything other than very simple.
A very good source of reference is the CRA's website. http://www.cra-arc.gc.ca/formspubs/tpcs/dcsd-eng.html The T4011 is the detailed guide.