Why fossils have been given a minimum age of 10000 years? Can a naturally preserved remain of ancient life be considered a fossil if it less than 10000 years but show excellent preservation?

The term "fossil" is not completely binary. Some bones are fresh, some are fossils, and some are in an intermediate state known as "sub-fossil". You are right that the rate of fossilisation can vary enormously depending on the environment. In some cases, fossilisation can complete in a small number of millennia; in others, proteins survive intacts after tens of millions of years.

Just to add: the cutoff of 10,000 years was largely established for practical purposes of dividing disciplines into palaeontology and zoology/archaeology, but has no basis in reality (I know, I'm being a bit sarcastic here).
The age is based on the start of the Holocene.