Note the double space in bash's error message before "grep": that probably means you've typed an unbreakable space (AltGr+space), which can happen quite easily if your keyboard requires AltGr to produce the pipe symbol.
Try dropping the spaces around the pipe symbol:
ps aux|grep xscreensaver
In your updated examples:
[root@Hostname ~]# ps aux | grep xscreensaver
bash: : command not found...
bash is trying to run the "unbreakable space" command, which doesn't exist; hence the error message, "unbreakable space": command not found...
[root@Hostname ~]# ps aux | grep xscreensaver
bash: grep: command not found...
bash is trying to run the command whose name is "grep" preceded by an unbreakable space, which doesn't exist either; hence the error message with two apparent spaces between "bash:" and "grep".