Unless you have solid evidence it was done and the date / mileage you have to replace the belt. If not now, when? But you can be pretty sure it was not done. People often sell cars in lieu of replacing the timing belt because the belt replacement is so expensive and does not add anything to the market value of the car.

Most repair shops will put a sticker on the timing belt cover up high by the cam shafts giving the date and mileage of the change. Call the shop where the logbook says the work was done and ask. Most good shops have electronic records and they'll pull it up.

Pretty hard to say, You can not really tell buy looking. They all look brand new to me after almost any distance. But I will bet that the previous owner said "Why bother changing it, I am just going to trade it in." The dealer you bought it from probably did not see any profit in replacing it.

If you want to sleep better, you should pay to have it replaced.

Does it SAY in the service logbook where the maintenance was done? If so, inquire at that shop.

Look for RTV-type sealant around the cover

I am the 2nd owner of a 2001 Hyundai Grandeur. I bought it when it had done over 125,000kms. It is now on about 135,000kms. I took it to get a minor service yesterday and the mechanic said the timing belt would need to be replaced if it hadn't already. I did not know how to check if it had already been done. My service logbook from the previous owner was last signed to have been serviced at 90,000kms (though written 85,000kms at time of service)...would the timing belt have been replaced then? Or would it have had to have been replaced before sold to me? I'm not sure how else to check and would prefer not to pay a large amount to replace something that may have only newly been replaced, though I am aware if it broke the cost would be much higher to fix the engine/motor.