Where can I find the application executables in the filesystem?

The complete answer is to check out the Filesystem Hierachy Standard documentation on what stuff goes where.

But in your case, if you want to know where a particular executable is (for example firefox) use

which firefox

And you will get the full path like this

/usr/bin/firefox

Applications installed through the package manager usually go to /usr/bin. Applications you compile yourself go to /usr/local/bin/ unless you explicitly set a different prefix when compiling.

You can find out where a specific application lives by typing which application_name into the terminal. E.g. which firefox will print /usr/bin/firefox (if you're using firefox from the Ubuntu packages).

A good CLI commad for this kind of questions is:

whereis <nameofwhatever>

or, of course which (see below)

You can also try this if you're looking for the executable from a package name:

dpkg -L firefox

This will list all files owned by firefox. To get the executables, pass it through further processing

dpkg -L firefox | while IFS=$'\n' read -r line; do
    [[ -x "${line#*:}" ]] && echo "$line"
done