Corolla with 1.6 4A-FE Oil burning

Yes you should worry, you aee burning oil, it could be your piston rings are going. With the age of the car and what it would cost to repair it, it not worth it. There are oil additives that will help but not cure the oil burning. You can use a heavy weight oil on you next oil change...

I would not worry much. A little oil consumption is not a big deal, Your oil usage is about 1 quart in 1,800 miles which is not ideal but you could still get another 100,000 miles on that engine. I would probably go to 10W-40 and see how that works. I have found that changing oil more often reduces oil consumption on high mile cars. I recommend changing oil every 3,000 miles. (4,800 km)

What can we say about the 4A-FE engine itself? I know the service history and I have the actual service booklet and it has been handled well before. Is the 4A-Fe engine prone to burn some oil or am I alone with my problem?

Here is a suggestion and take it for what it is worth. This has worked well for me on high mile cars that use some oil. When the oil is changed let ALL the oil drain out even if it takes an hour. Change the oil and filter no more than every 3,000 miles. The object is to get the engine CLEAN inside as dirt can cause the oil control rings to stick and not work like they should. Monitor the oil consumption, I think you will find that when the oil is clean the engine will not use much oil but when the oil starts getting dirty the oil consumption will go up. You might want to try Liqui-Moly engine flush, I can't vouch for it but I plan on trying it as their other products are very good.

You don't say what oil you use but high quality oil may give you less oil consumption. If you research oil online look for oils that have fewer volatiles as they will not evaporate like lesser oils. http://www.acculube.com/hd-faq-synthetic-oil-advantages.html

Back in the old days you could add thicker oil to an engine and it would slow the oil consumption but in the high tolerance present day engines you are better off replacing the 5w30 oil more often than causing low oil pressure caused by the oil being too thick to circulate the engine. adding thicker could slow oil usage but it will starve the circulation of the oil.