Question 1: Am I correct when I say that my CPU provides up to 16 PCIe 2.0 lanes (direct link from PCIe slot to CPU)? Either 1 slot at x16 speed or 2 slots at x8 speed each.
Yes, per the Intel data sheet for your i7-2700k, the processor itself supports a maximum of 16 PCIE 2.0 lanes. More lanes are supported through the DMI interface and the Z68 Express Chipset.
My secondary goal is to determine if I can improve my SSD read/write speed in my old build by upgrading f.e. to an NVMe PCIe based SSD or that I have to buy a new Motherboard and CPU as well.
You can get a PCIE card for an NVMe M.2 drive if you want. You can read this article
about how the PCIE 2.0 speed will compare to a PCIE 3.0 slot. Sequential read/writes are definitely faster with PCIE 3.0, but with other types of reads/writes, not so much difference. Both are a lot faster than the PCIE SSD compared in that article.
Question 2: My motherboard furthermore provides 4 PCIe 2.0 lanes (Not direct to CPU, but rather over the Z68 chipset) ?
The Z68 chipset on your motherboard provides up to 8 PCIE 2.0 lanes. It appears from your motherboard doc that the PCIe x16_3, PCIe x1_1, PCIe x1_2, USB3_34 and eSATA ports all share bandwidth which likely means they are all supported by the Z68 chipset which means they all connect to the processor through the 20GB/s DMI channel (so no direct connection themselves to the processor, but connect through the DMI channel).
Question 3a: Where does the 16Gbytes/s come from on the block diagram <<see link above>> on the x16 slot ? I thought PCIe 2.0 offers 500 MB/s per lane (= 8.0 Gbytes/s for x16) ?? <<see PCIe speeds link above>>
Your processor isn't supporting all the direct connection PCIe lanes communicating at full speed at once (which wouldn't actually happen very often in the real world anyway). So, the total bandwidth available is less than sum of the max bandwidth each lane is capable of.
It's kind of like connecting 10 PCs to a router each with a 100Mbps connection and the router has a 500Mbps connection to the internet. Each PC individually could transfer data to the internet at 100Mbps, but all 10 couldn't do it at once. If they were all trying to do max transfer at once, they'd end up sharing the 500MBps connection to the internet and each running about half speed.
Question 3b: Same question as question 3a. If i assume the lower 'b' here in 5 Gb/s stand for bits (does the 'Gb' stand for Gbits/s and the GB for Gbytes/s ??), this would make sense since 5 Gbits/s = 625 Mbytes/s (500 Mbytes/s if I take the 8b/10b decoding into account). And 500 Mb/s is what I find to be the speed of PCIe 2.0 per lane in the << PCIe speeds link above >>.
That is the usual convention for Gb/s and GB/s.
Question 4: Does my motherboard support NVMe protocol ? OR only AHCI protocol ? (I assume it doesn't support NVMe since it is way old)
No, it doesn't support NVMe directly. That's what you would get the PCIe add-in card for. I don't think NVMe was even around yet when your motherboard was manufactured.
Question 5: I read a lot about the fact that PCIe slots can be connected to the CPU using PCIe lanes OR SATA III connection. It depends on the MB manufacterer. Is this true and how can I check this ? My MB manual doesn't specify it.
That's not really the correct way to think of it. PCIe slots can be connected directly to the CPU or they can be connected to some other chipset that communicates with the CPU a different way. In the case of your motherboard, there are 16 lanes of direct PCIe connection to the CPU and the Z68 chipset offers 8 more lanes that connect to the CPU through the DMI channel (all sharing that channel).
SATA ports are also connected through the Z68 chipset and also share the DMI channel to the CPU. The Z68 chipset supports 2 6.0Gb/s SATA ports and 4 3.0Gb/s SATA ports. The other two 6.0Gb/s SATA ports on your motherboard are from another added chipset (A Marvell PCIe SATA controller). From the notes in your motherboard, it appears these are sharing PCIe lanes with some other devices (meaning when one is in use, the other device is disabled).