All PCIe SSDs support any number of PCIe lanes. Both devices and slots are intercompatible providing you can find a card that will fit. Most native PCIe SSDs are fairly expensive and require a larger slot, so you will need an open-ended x1 slot.
M.2 SSDs don't fit into PCIe directly but you can get cheap, passive adapters like this one, though obviously you would need to look for one that is x1 if you do not have an open-ended slot.
Whether PCIe x1 is faster than SATA (there is no such thing as a "DATA connection") depends on what version of PCIe you have and what version of SATA you have. The following is a brief summary of speeds:
So if you have 6Gbps SATA and a PCIe v2 slot then no, it will not be faster (of note, all southbridge PCIe slots on Intel boards before Skylake are PCIe 2.0 only)
Your most important concern though should be whether your BIOS/EFI can boot from a PCIe SSD. Most older boards (>1 generation or >= 2 years) cannot boot from a native PCIe SSD so you must have a SATA SSD or HDD to boot from.