What noun is in this sentence the tree was old?
The noun in the sentence is tree, a word for a thing.
The noun 'tree' is a common noun, a general word for a type of plant. The noun 'tree' is capitalized only when it is the first word in a sentence. A proper noun is the name of a specific person, place, or thing. A proper noun is always capitalized. Examples of proper nouns for the common noun 'tree' are Tree Street, Columbia SC or Oak Tree Academy, Tyler TX.
How many nouns does this sentence have David carefully climbed the ladder to pick the grapefruit at the top of the tree?
The nouns in the sentence are: David (proper noun), the subject of the sentence; ladder (common noun), direct object of the verb 'climbed'; grapefruit (common, compound noun), direct object of the verb 'to pick'; top (common noun), object of the preposition 'at'; tree (common noun), object of the preposition 'of'.