I have 3rd gen Intel mobile CPU i5-3210M, with integrated HD4000 graphics.How can I tell what driver version (i915) I have and does it support Vulkan? What Mesa version I have in Kubuntu 16.10?
What happens if I run a game made with Vulkan API without Vulkan support in driver?
A simple way is to look the unofficial Vulkan Hardware database.
The best way is to install the vulkaninfo utility from your repository manager with sudo apt install vulkan-utils. This package provides utilities for Vulkan, including vulkaninfo.
Support does depend upon hardware, though most of the GPUs made in the last decade are compatible. Then, it needs support from the kernel, GPU drivers, and game (or other software).
I'm afraid that your GPU, Intel HD 4000 (Ivy Bridge), has extremely limited and somewhat broken Vulkan support, due to hardware limitations.
Installing and using vulkaninfo
Vulkan has a standard set of tools available for all platforms. On Ubuntu this is available by installing the vulkan-tools package.
You can then use vulkaninfo to see detailed information about your Vulkan installation. I'd advise running it with vulkaninfo | less or piping its output to a text file as it can be large.
You can see the available Vulkan-supporting GPUs on your system in a couple of places here. For example the Presentable surfaces section has a subsection for each Vulkan-capable GPU you have.
It's important to know that a GPU called llvmpipe or softpipe is a software-emulated vulkan device. Thanks to the hard work of its developers it is possible to use vulkan without any dedicated hardware by translating it using llvm into native CPU code - but as expected it's much slower. Low-demand 3d software could still use Vulkan, but it's almost certain unsuitable for things like gaming. If that is the only Vulkan device listed, then your dedicated hardware doesn't support Vulkan, or its driver isn't properly installed and working.
If you don't even have llvmpipe, then it's possible Vulkan itself isn't properly installed (libvulkan1 and mesa-vulkan-drivers).
Finally, if you use Vulkan in 32-bit apps it uses a different Vulkan loader and Vulkan drivers, so you should install and check the 32-bit vulkaninfo in such a case.
According to Intel: (Intel open source graphics drivers and vulkan graphics api) support for Vulkan is seamlessly built into Linux PC distributions.
Whether or not Vulkan or OpenGL support is built into a given game is up to that game's developer not to your hardware/firmware or software drivers.
As comment below points out the above "seamless" integration is for 6th generation CPUs. For IvyBridge (HD4000) and newer Vulkan support it is built into Mesa 13 Intel-Vulkan driver that can be downloaded here: (archlinux.org vulkan-intel) and is discussed in detail here: (Mesa 13). Note Mesa driver 13 was released November 1, 2016 and is a great improvement over version 12.
It appears that if the GPU isn't running an ancient driver, it mostly definitely supports Vulkan.
So you can check if the old "radeon" driver is in use with:
lspci -v | grep --after-context=12 VGA | grep "Kernel driver in use:" | cut --delimiter=":" --fields=2 | xargs | grep --quiet --invert-match "radeon"; echo $?
