|"I’ve read that without AHCI and NCQ support an SSD would start to slow down and accumulate garbage. Is it true?"|
Not sure about AHCI, but I've read that SSDs really take a hit in performance without NCQ.
"PCI Express 1.0 offers maximum per-lane data rate of 250 MB/s. Is it really so? Would I get that maximum speed of 250 MB/s when using PCI-Express x1 to SATA 3 controller?"
Your max transfer rate will be somewhere between 200 and 250MB/s. While this is nowhere near the speed of SATA3, you'll still get a significant boost in speed over a mechanical hard drive. Standard hard drives absolutely suck at random access and will often dip below 30MB/s.
"By the way, in my case does it matter which controller PCI-e to SATA 2 or SATA 3 I would use?"
You'll want to make sure that the card you choose allows you to boot off the attached SSD. From what I've read, some PCIe SATA controllers don't.
"Both of them support NCQ, but how do I know that these controllers support AHCI?"
AFAIK, if a controller supports NCQ, then it supports AHCI.
"My motherboard’s southbridge is ICH6 which has an integrated SATA 1 controller that supports data transfer rates up to 150 MB / s. Am I able to increase this rate by using an expansion card controller?"
The BIOS/firmware on the card will not upgrade your board's integrated controller in any way. All of your ICH6 ports will continue to run at 150MB/s without AHCI.
I know this has nothing to do with the topic at hand, but are you sure your video card is in an AGP slot? The i915 (and your board) only support PCI-E.
HTPC/file server | Pentium M 780 @ 2.82GHz | 4GB | Radeon HD5750
120GB SSD + 2TB/3TB/4TB | Blu-Ray/HD-DVD combo drive | Win8 Pro