I think I healed some of the sun sized spots in the photo, but I did not touch the second photo. Is this the defect of the lense? I think those started appearing after one time I used the camera in rain. The lense is the cheap one that comes with sony a-6000. Those spots appear only in certain light conditions, so hard to reproduce. Could it be due to unclean lense? Or maybe even matrix?
This looks like sensor dust. It probably is. The reason that it appears only in certain conditions is that dust spots get larger with a smaller aperture. Since you were shooting into the sun, the camera had no choice but to set a very narrow aperture and it made your sensor dust more visible.
This is easy to test. You stop down the aperture yourself, increase EC to +1.5 and shoot a white wall. The dust will be there and always at the same place. Do the same shot at F/3.5 and it will either not be visible or will be much smaller. Have you sensor cleaned by a professional to avoid risk of damaging it but you can learn later how to do it yourself with the right products.
Sometimes a spot of water inside the lens will look like that but it will eventually move and dry, so you will not get as consistant an issue as with sensor dust.
...or in the interim, you could add the dust information in camera so the camera remembers and handles the dust blemishes and compensate in your recorded photos.
Ref: Canon function is "Dust Delete Data" http://learn.usa.canon.com/resources/blogs/2013/20131105_stoner_dustdelete_blog.shtml