In Full recovery mode, when does the buffer/transaction log changes get applied to the database data pages?
According to the SQL Server Transaction Log Architecture and Management Guide, data pages are modified in cache first (logical write). This occurs the same way regardless of the database recovery model, with only the level of logging detail being different. A transaction log record containing the modification is created and written to the log buffer cache. These log buffers are always physically written to disk before the modified pages (write-ahead logging).

Data pages may be written to disk by lazy writing, eager writing, and the checkpoint process. The log buffer is flushed to disk before the corresponding data pages are written to the data files by these processes.

Transaction log buffers are physically written to disk when 1) they become full, 2) during COMMIT when the log buffer contains data for a durable transaction, 3) a checkpoint, or 4) a modified page is written to disk by one of the aforementioned processes.