Yes, your understanding about the available number of PCIe devices is correct. However, it doesn't necessarily mean you can have as many NVIDIA GeForce RTX 2080 Ti GPUs.
Are # of PCIe lanes associated with the processor or the chipset in the motherboard?
Both. In modern computers, both CPU and motherboard (the South Bridge, SB) can have PCIe connectivity.
As you presented a Z370 MB, I'm taking Intel Core i7-8700K as example. According to Intel ARK, it has 16 PCIe lanes built in, which is very likely connected to the two PCIe 3.0 x 16 SafeSlots. This means you can have at most 2 PCIe devices that can communicate with CPU directly. The other 8 PCIe lanes (1x4 + 4x1) belong to the SB and are intended for peripherals like NVMe SSDs or network cards.
That doesn't mean you can't connect RTX 2080 Ti GPUs to the SB, however. Continue reading these answers to more questions.
How many PCIe lanes does a Nvidia 2080 Ti graphics card need?
This depends. If you're using those cards for machine learning or cryptocurrency mining, a single PCIe lane may suffice. But I haven't heard someone using fresh flagship card for those tasks, so I'm assuming you're using them for gaming.
For gaming, it's best for the RTX 2080 Ti card to run on full PCIe 3.0 x16 speed, as it will maximize the utilization of its outstanding performance. Running such a card with only 8 lines is likely limiting its potentials, as the data transfer rate is going to be the bottleneck when processing high-quality textures, or other I/O intensive tasks. If you lower some expectations, you may stand its performance under only PCIe 3.0 x8 speed.
How can these lanes be split? As in the above example board
If you don't get some extra pieces of hardware, you have only two options: 1x16 and 2x8 for the CPU lanes, and 1x4 for the SB lanes. This is because only the two biggest slots are connected to the CPU, so you can split the CPU lanes to at most 2 devices. The last big slot can also be used for a 3rd card if you like.
Without additional hardware, you can have at most 3 cards on that board, as there are only 3 "big slots" on the board (also take into account there's no RTX 2080 Ti GPU with single-slot thickness). But with some splitters you may be able to get more. See this thread for more information.
Yes, you are right, but remember: PCIe gen4 x4 is 8GB/s. It is very, very difficult, to saturate this, even with 2 SSDs. Most SSDs are much slower. Like reading with 3.5GB/s is fast, but that would be 7 of 8GB/s. Still 1GB/s left for USB3 - wich usually is much more than enought. This would saturate at least 5 modern HDDs at the same time. Or almost 2 SATA 3 SSDs.
Don't be affraid of that. PCIe also is much less CPU intensive than SATA - this all contributes to much better real life performance. You will not notice a bottleneck. You could in theory reach it, but it is very, very unrealistic in reality. :D
Have fun with your nice Setup.
Best Answer
PCI-E slots can have 1, 4, 8 or 16 lanes. A CPU supports a specific number of lanes.
The term "lane" is used because each lane is not shared with any other device, and this is why it's faster than standard PCI. I/O bandwidth on the older PCI standard was shared amongst all devices on the bus. A device like a PCI graphics adapter or heavily utilized Ethernet adapter could saturate the bus, leading to contention and slowdown. One of the reasons AGP was developed was to basically put the graphics card on its own 1-device bus.
Obviously, more lanes = more speed. Graphics cards are typically 16x.
A card can be put in a slot with less lanes than it needs (if motherboard components don't get in the way), but it will operate slower. A card can be put in a slot with more lanes than it needs, but you lose the extra lanes. It won't make the device any faster.
Some chipsets do weird things with PCI-E lanes. I've heard of some motherboards (will update if I find the info) depending on the type of cards you have in other slots, a 16x slot may become an 8x slot.