Choose the option which correctly fills the blanks: " having her lunch, she stood the tree...

The sentence requires a temporal preposition for the first blank, a spatial preposition for the second, and a preposition of purpose/expectation for the third. 'After' indicates sequence, 'under' describes the position relative to a tree, and 'waited for' is the standard English phrasal verb for expecting someone.

Step-by-step Derivation:
Step 1: Analyze the first blank ('_________ having her lunch'). The phrase describes an action following another. 'After' is a temporal preposition that fits logically. 'With', 'Inside', and 'About' do not make grammatical or logical sense in this context.
Step 2: Analyze the second blank ('she stood _________ the tree'). A tree provides overhead cover. 'Under' is the most natural spatial preposition. While 'below' (Option A) is technically possible, 'under' is the idiomatic choice for standing beneath a tree's canopy. 'Further' and 'across' do not fit the context of standing by a single tree.
Step 3: Analyze the third blank ('waited _________ him'). The verb 'wait' requires the preposition 'for' when referring to a person being expected. 'Wait for someone' is the correct idiomatic expression. 'Wait to' (Option C) would require a verb (e.g., 'wait to see him'), and 'wait into' (Option D) is grammatically incorrect.
Step 4: Combine the selections: 'After' (Temporal) + 'under' (Spatial) + 'for' (Expectation) = 'After having her lunch, she stood under the tree and waited for him.' This forms a coherent and grammatically correct sentence.