Could gazing at home led light or ice cold compress on eyes afterwards lead to retina or cornea damage causing blurred vision of bright objects?

Not usually.: But, of course, it depends on how bright the light and how long you stare. Cool compresses are even less likely to cause these problems. If you are having changes in your vision, please see a board certified ophthalmologist in your area for a quick examination. Eye sight is a precious thing, and should be protected.

Yes it damages : Led light saves energy , gives brighter long long bulb life , it emits in blue spectrum band, direct visualization will cause damage to retinal cells , they once damaged will not grow back ( permanent damage ) not looking directly and use of dark glasses will protect to some extent , see your eye doctor for exam & to check visual fields.

Yes, no: Starring at a light for a long time, depending on how bright the light is, can cause retina damage, but it would be very rare. Cold compresses are safe, but you do not want to freeze-damage your eyelids or cornea, so use some caution.