Countable nouns refer to a thing or 'things' (singular or plural), while uncountable nouns refer to 'stuff' (always singular). Like many nouns - such as 'tea' or 'wool', for example - 'bark' has both a countable and uncountable form. In most cases, you see 'bark' in its uncountable form : bark is 'stuff', the hard material that you find on the outside of tree trunks. In most of your sentences, 'bark' is uncountable as it refers to the substance. However, in your fourth sentence, "Barks of different trees have different characteristics", it is countable and plural: this is because 'barks' is a shorthand way of saying 'types of bark'. All uncountable nouns become countable when you're talking about 'different types of...'. For example, 'tea' is uncountable, but when you say 'We sell a variety of teas', the word is countable because you mean 'different types of tea'. I hope that helps.

The bark of a tree is uncountable, but the different tree barks in a pile of tree bark, or tree bark scattered on the ground in a forest would be countable by a scientist if they wanted or needed to count the different species of tree bark.

If I understand your question I would say the word bark (tree bark) is not countable. You would not say 4 barks. You would say 4 pieces of bark. The sentences generally seem fine.