I just want to ask:
Are applications cross-compatible with each any Linux System? For example the Suse apps can be installed in RedHat or LindowsOS or Mandrake, and vice versa to each any Linux system?

Thanks.

Usually yes. But you may have problems with interdependencies on shared modules if a library has had functionality removed or changed significantly over time (which may break either the new application or worse your entire OS).

Always be careful about that, it may happen at any time (also when installing applications that are compiled for a newer of older version of the flavour you're using now...).