Can I run Ubuntu desktop x86 applications On Ubuntu For Android? This may be a fairly simple question, but I want to be sure.  My guess is that it can't be done.

Question 1: For example, I have an executable for Linux (no GUI , just cmd line , it just makes some computations) and it works well in my x86 desktop and I want to be able to run it in my Android tablet. The tablet is running Ubuntu for Android. Is it possible to run the executable in the Ubuntu environment on Android?

Question 2: I have a standard commercial Linux app and I want to install and run it on Ubuntu for Android. Is that possible?

If it's not possible, is there any workaroud to this?
No, you need ARM executables (or whatever the underlying architecture of your device may be).

The only way to get around it, apart from compiling from source or finding an ARM version of the package, would be some sort of virtualization.  I don't know of any virtualization tools built for ARM myself, but at least some versions have virtualization extensions so there is the possibility of hardware-accelerated VMs.