For stability, is there a limit to the sovereign debt that a Government owes to itself against issued fiat currency? Looking beyond the optical illusion of Governments owing debt to Central Banks, Governments effectively owe themselves the sovereign debt created against issued fiat currency.
By definition, there shouldn't be any limit to the debt that an entity owes itself.
Does this mean that Governments can continue to print a limited amount of fiat currency (say 5% of GDP) annually forever?
In other words, is there a problem even if this debt that the Government owes itself, grows to, say, 1000 times the GDP over centuries?
Does this mean that Governments can continue to print a limited amount of fiat currency (say 5% of GDP) annually forever?

Yes government can 'print' (I use quotation marks because most money is created electronically nowadays) any amount of fiat currency it wants to.

In other words, is there a problem even if this debt that the Government owes itself, grows to, say, 1000 times the GDP?

Depends on your definition of a 'problem'. In terms of affecting probability of default it is not any problem at all. Central bank can scrap all the government debt it owns at a stroke of keyboard.
However, this being said, it is agreed by virtually all conventional economists that increasing amount of money (ceteris paribus) leads to inflation (see Mankiw Macroeconomics 8th ed.). So eventually if government would try to create arbitrary high amount of money it would eventually lead to inflation and at some point even hyperinflation. For this reason it is generally agreed by economists that governments can fund arbitrary amount of spending by creating new money (see this poll among the most prestigious policy economists). This being said there would be some scope for generating seigniorage revenue that way, so monetary financing might not be bad if it is done carefully, but having debt to GDP ratio of 1000:1, completely financed through central bank's high powered money, would likely lead to disastrously high inflation.