Not only does it still exist, devices running 32-bit Windows 10 are still actively sold. I purchased one in 2016 (Intel compute stick) and another in 2017 (Ollee D1016W).
Both have 64-bit capable Atom CPUs, but were deliberately shipped with a 32-bit userland (presumably to save on disk space).
While technically correct sth. like the Quark is probably not what he meant but some earlier models of the Atom lineup (<= 10y, 2008 onwards) are 32bit chips. There are chips released as late as 2011 [1] which lack 64 bit support.
No they don't, unless you're somehow running Windows 10 on a 32 bit machine.
Been bitten a few times by programs bundled using ancient 16-bit InstallShield. It _does not_ work on Windows 10.