How to check which kernel I am using?

The uname command will allow you to check the kernel release (version):

How to find the package which provides my kernel or any other kernel on Ubuntu/Debian:

On Centos systems:

Alternatively you can search the packages list on the websites below:

For Centos - http://mirror.centos.org/centos/7/os/x86_64/Packages/

For Ubuntu - https://packages.ubuntu.com/

Do kernel updates require every version in between?

If you have a system which have not been updated for quite a while then the package manager is likely to skip to the latest available kernel package, provided there is no package conflicts.