Pokémon hacks fail for a boring reason: the base dump is a different revision from the one the patch hashed. I publish the SHA-1 values the pret repositories use as build prerequisites. FireRed US 1.0 is 41cb23d8dccc8ebd7c649cd8fbb58eeace6e2fdc. FireRed US 1.1 is dd5945db9b930750cb39d00c84da8571feebf417. Emerald US is f3ae088181bf583e55daf962a92bb46f4f1d07b7. Those are the numbers I will repeat on the detail pages. I will not estimate a hash for a hack whose author did not publish one.
FireRed, Emerald, and Lazarus have their own pages. For Unbound, Radical Red, Gaia, or a HeartGold project, use the current author readme to identify the exact game and revision. The patch format follows the hack. Many are UPS or BPS. The accessible Lazarus guide says BPS; that format claim is marked as one source on its detail page.
This site does not host the games or the patches. You bring a dump you already have, compare the hash, and apply the author's file. A source checksum error is the tool protecting you from the 1.0 versus 1.1 mixup. The home patcher is the button. The GBA page explains why save-chip patches are a different download.
Related pages: FireRed, Emerald, Lazarus, the UPS guide, and the GBA console guide. If a table cell is blank, I did not have a figure to put there.