The main target of updating BIOS is supporting Core2 Duo. I'm not so sure about 4GB RAM. I remember that some notebooks from same era (and same chipset) did need BIOS update to support 4GB ram. Specifically Fujitsu-Siemens Amilo Xi1546 was the same model as some Alienware notebook (just different logos, stickers and BIOS). So Fujitsu-Siemens BIOS was stuck at 2GB max, but updating to Alienware BIOS there was 4GB RAM unlocked possibility, which was comical.
But i see no evidence that BIOS update will bring you 4GB possibility. However it will unlock much faster 64-bit Core2Duo.
I update BIOS on many things including: notebooks, All-in-One computers, motherboards, SSD, and even DVD-RAM drives! So my experience is telling me to save your current bios, so, maybe, you could return to it, if new bios will be worse to you. You can use bios saving and update programs, my favorite from that era is WinFlash 1.94 - i saved many old bioses (and returned to them) using that program. I don't know if it compatible to your notebook, cause it have AMI bios, you can Check Soggi's archive about updating bios on vintage systems.
I found topic about your laptop: Official S96S Owners Lounge as you can see on link not everyone like BIOS update, cause it make notebook more noisy (probably more aggressive fan settings, cause Core2Duo is more hot then it predecessor). I recommend to read that topic - maybe you will find something interesting.
Even that you bring speed results in text which is hard for me to decode (i asked screens). It is obvious to me that ASUS laptop work with SSD in SATA-1 (150) mode, while HP Win7 laptop run in full speed in SATA-2 (300) mode. I have similar problems on my nForce 4 system which is also SATA-2 system, but in my case refuse to work with HDD in SATA-2 mode, even after i install native nvidia drivers. So i have NCQ, but not SATA-2. I never manage to solve this problem. Maybe in your BIOS there is a switch to SATA-2 mode? Maybe it will be after BIOS update?
I suggest just install all drivers for your Intel motherboard in usual auto mode and not install them manually. Just run installation program and let it install automatically.