Will Linux write out the above dirty pages in order or is there a chance they they'll get written out of order?
Não tenho certeza.
If out of order writing is a possibility, how do databases and applications that generate log files handle this?
SQLite assumes that the underlying filesystem can reorder write requests and that the page count can be burned into oxide first even though its write request occurred last. So as a second line of defense, SQLite also uses a 32-bit checksum on every page of data in the rollback journal. This checksum is evaluated for each page during rollback while rolling back a journal as described in section 4.4. If an incorrect checksum is seen, the rollback is abandoned. Note that the checksum does not guarantee that the page data is correct since there is a small but finite probability that the checksum might be right even if the data is corrupt. But the checksum does at least make such an error unlikely.