They're not saw filters. The "big one" is a ceramic duplexer and the second smaller one is a ceramic filter. They split the antenna signal into the "Uplink/TX" and "Downlink/RX" band, and isolate the sensitive RX stuff (that tries to receive very faint signals) from the TX stuff (which transmits like 1W or 2W of RF power into the antenna).
In more modern phones, there is no duplexer for GSM. Simply because GSM has been designed specifically so that a phone doesn't need to be full duplex. The TX and RX slot are slightly shifted in time and so modern phone just have an antenna switch. I guess back in the days those switch weren't good enough ...
And that weird module you took apart, I would guess that it's the RF Power Amplifier.