I want to install and run executable files and apk files in Tails; is there a way to do so?
There is no supported way.
.exe files (or PE files) are Microsoft Windows executables, which can't be natively run on Linux (which uses ELF files).
.apk files are Android application packages, which are a zip file containing some Dalvik machine code and various other resources are intended to be run an the Dalvik VM which Android uses, and aren't natively supported on Linux.
To run either of these you'd need some form of emulator, which Tails doesn't supply and the installation of which might break things in unexpected ways. See the warnings on the Tails website about Additional Software. As Tails can't properly test every possible software package, they can't make any guarantees about what will or will not work or break.