Your question(s) do not have a simple answer. It depends on many things.
The ROM likely is programmed at the factory and can not be changed. But in some micros it can be erased and reprogrammed. (depends on computer)
The EEPROM likely is programmed with defaults at the time when the ROM is programmed. When the TV is first powered up it looks bad, and every one looks different. In the factory there is a process of calibrating or aligning the TV. Here the size and shape and colors are set to look right. Then these new values are stored in EEPROM. Later at your house if you want the picture to look bigger/smaller/brighter/...…. then new values are added.
If EEprom data is corrupt
There are many different answers, again.
Some TVs do not have a way of knowing if the data is corrupted. They would just use the bad data and the picture looks bad. Simple!
Some TVs do know if the data is corrupted. They would just not turn on.
Some TVs will load the default data. Like you said.
Some of the TVs I designed, we loaded into EEPROM the average of the last 1000 TVs. What values that made the last TVs work are averaged and used on the next TV. Some factories did not do this step.
Then we aligned the TV and stored the values for this TV.
Next the used can change some of the values.
If the EEPROM gets corrupted we can back up to the values as the set left the factory.
In some TVs we stored the "default" values in ROM so they could not get corrupted. At power up the computer tests to see if the EEPROM is blank or corrupted and if so copies ROM values to EEPROM. (these values are not good but better than nothing)
Hope this helps. Ron,