Learn Russian: Если бы не твой вклад, проект бы рухнул. - If it weren't for your contribution, the project would have collapsed.

The phrase если бы не is a fixed construction meaning 'if it weren't for' or 'were it not for'. Even though it contains the negative particle не, it always takes the Nominative case for the thing or person being discussed. You don't need to apply the usual negation rules here.

Could the second half of the sentence be written as проект рухнул бы?

Yes, absolutely. The conditional particle бы is quite mobile. It usually gravitates toward the front of the clause or attaches to the emphasized word. Placing it after the subject (проект бы рухнул) or after the verb (проект рухнул бы) are both perfectly natural and mean the exact same thing.

Does the verb рухнул only apply to physical structures collapsing?

No, just like the English verb 'collapse', the perfective verb рухнуть is frequently used figuratively. While a building or a roof can рухнуть, so can abstract things like a project (проект), the economy (экономика), or someone's hopes (надежды).

How do we know this translates to 'would have collapsed' instead of 'would collapse'?

Grammatically, you don't! Russian uses the exact same form (past tense verb + бы) for both present/future conditionals and past conditionals. The translation depends entirely on context. Since a 'contribution' to a project is usually something that has already happened, 'would have collapsed' is the most logical interpretation here.