I personally have never read of any of the claims you're referencing. However, the Hagia Sophia was converted into a Catholic Cathedral during the crusader occupation and most of the orthodox icons were melted down for its base gold or carried off to Venice. Also, there isn't much to read about the Imperial Palace at the time from the sources available to me, as the Latin Emperors didn't even reside in it during their occupation of the city due to the damage sustained to the main palace during the sacking, but instead they resided in the Boukoleon Palace along the southern shore of the city.

In any event, the sack of the city and its following occupation damaged the city's wealth and position in the region to the point where the population plummeted from over half a million to just around 50,000 people by the time the Byzantines returned in 1261.

The sack itself sent shockwaves all around the region as regional trade was disrupted, but the occupation of the city afterwards for the next 55 years was the most destructive to the city's position in the region to the point where the damage was irreversible. The Latin's embezzlement of the city's wealth and mismanagement of administration crippled the city's position in the region beyond repair, and many monuments and other sources of wealth for the city were carted off and sent to Venice (The bronze chariot statutes of the Byzantine Hippodrome are still mounted in Venice to this day)

Before the sack, Constantinople was run by an elaborate system of Imperial bureaucrats who handled the basic operations of the city such as collecting tariffs from trading ships, tax collection, distribution of food to the markets, etc. that preserved the wealth of the capital. The Latin Emperors deeply distrusted these administrators and often accused them of disloyalty to their state, and eventually the entire system of bureaucrats was disbanded in fear of them overthrowing the Latin Emperor. This was a disaster for Constantinople as this paralyzed all trade income, distribution of food and water, and tax collection to the point where the city had only a small fraction of its former wealth by the time Michael VIII Palaiologos recaptured the city in 1261. The returning Byzantines did attempt to restore the city after their reconquest by reinstalling the old bureaucrats and restoring basic administration of their capital, but the damage and loss of material wealth during the Latin occupation was too damaging to make a full recovery.

Source:

Jacobi, David, "The Latin Empire of Constantinople and the Frankish States in Greece", in Abulafia, David, The New Cambridge Medieval History, Volume V: c. 1198–c. 1300, Cambridge University Press. 1999 pp. 525–542,