Is there a way I can view live server activity via SSH. Like failed logins, apache errors, etc?

Poor Man's System Monitoring:

Get gnu screen. Create N terminals in screen where N is the number of things you want to track.

In each terminal do:

tail -f /var/log/<log file for what you want to track>.log

So to view many general events I would tail syslog like this:
tail -f /var/log/syslog

We can certainly get more sophisticated than this but this does give you a live view of what's going on on your server with minimal setup.

A couple refinements:

Using -F instead of -f will entice tail to deal with log rotation; by default, -f follows the file by descriptor, instead of by name.

You can also tail more than file per incantation... e.g. you can "tail -F /var/log/syslog /var/log/exim4/mainlog". This is especially handy with web logs split across virtual hosts, like tail -F /srv/www/*/logs/access.log

But yes, tail is the bomb.

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It does not seen to be updating the screen as things happen.

I'm running

tail -F /var/log/{auth.log,apache2/{*-,}error.log,daemon.log,exim4/mainlog,fail2ban.log,debug,messages}

all the time inside a screen session, and I assure you it works as intended.
If you're planning to pipe it through grep before display, make sure to use --line-buffered argument to it.

Use these simple commands when you are inside your VPS hosting or dedicated server through SSH buddy -
tail -f /var/log/messages
tail -f /usr/local/apache/logs/error_log
To be noted that, if you are on a shared hosting account, you cannot run them as only 'root' has the above privileges .

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