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The adjective 'famous' is standardly paired with the preposition 'for' to indicate the reason for someone or something's fame. 'Famous in' or 'famous with' are not standard idiomatic expressions for this meaning. Therefore, 'famous for its beaches' is the correct construction.

The adjective 'affectionate' is followed by the preposition 'to' or 'towards' when directed at a person or group. 'Affectionate for' is a common error, but 'to' is the grammatically accepted preposition for expressing feelings directed at others. 'At' and 'with' do not fit this idiomatic usage.

The preposition 'by' is used to indicate the degree or margin of difference in measurements. When comparing heights, weights, or scores, 'by' correctly introduces the specific amount of the difference. 'In', 'at', and 'from' are not used to express margins of difference in this way.

To 'lean against' something means to rest your weight on it for support, typically a vertical surface like a wall or door. While 'lean on' is also used, 'against' specifically emphasizes the contact with a vertical barrier. 'At' and 'to' are not used with 'lean' in this physical sense.

'Beside' is a preposition meaning 'at the side of' or 'next to'. 'Besides' is an adverb/preposition meaning 'in addition to', which does not fit the physical action of walking. 'By' can mean near, but 'beside' is the most precise choice for walking alongside someone.

The preposition 'at' is used to indicate a specific location or a social event. Since a party is an event, 'at the party' is the correct idiomatic expression. 'In' is generally used for enclosed spaces, but 'at' is preferred for gatherings.

'At home' is a fixed idiomatic expression in English used to indicate that someone is in their place of residence. While 'in the house' is possible, 'in home' is not standard English. 'On' and 'into' are logically incorrect for this context.

The preposition 'since' is used with the present perfect continuous tense to indicate the starting point of an action that continues to the present. 'From' is used for general starting points but usually requires a 'to' or 'until' for a range. 'Since' is the specific choice for a point in time in this tense.

In a passive voice sentence, 'by' is used to introduce the agent (the person or thing performing the action). 'With' is used to introduce the instrument or tool used (the dagger). Therefore, 'stabbed by a lunatic' is the correct construction.

Case of prepositional usage.'Burning deck' is not an enclosure but a sort of platform. Thus, preposition 'on' is the correct usage.

Idiomatic usage. 'Man of might' means a man of strength, force, sway.

Case of prepositional usage. For sounds made by animals or things we use preposition 'of' after thier respective sounds.

Case of prepositional usage. It implies that all these roads are going towards Rome.

Case of prepositional usage. One teach something 'to' the other, and the other is taught 'by' the teacher.

Case of prepositional usage. Singing is a sort of sounds made by animals and birds. For animal sound we use preposition 'of'.