When to use a tpl.php file instead of a .css file?
If your real question is more along the lines of:


  Should I make the CSS conform to the markup, or make the markup conform to the CSS?


Then that's just a judgment call, there's no right or wrong answer. Go with what you feel comfortable doing. Some people love the plethora of classes Drupal adds by default, some people hate it. Some people prefer the Bootstrap approach (class, class, class), some people prefer the Susy approach (as few classes as possible, ostensibly). Neither is right or wrong, just different.

Read on for answers to the specific posed questions...


  When to use a tpl.php file instead of a .css file?


The literal answer to that is simply "never".

A CSS file and a template file are for different things, and contain different things. You wouldn't put markup in a CSS file, and you wouldn't put CSS in a template file (except perhaps in rare circumstances like if you were inlining the above-the-fold content or something).


  What are the problems and/or disadvantages of using a single .css file to make styling adjustments on my drupal site?


There are no problems or disadvantages per se. It's arguably better to split your CSS into multiple files, simply for modularity's sake, but those are all going to be aggregated back into one when the site goes into production mode anyway (assuming the CSS you're talking about is "every page" CSS; you haven't mentioned otherwise).

Basically go with what feels comfortable, by your organisation's standards, or whatever general advice you find and like about organising CSS files. Drupal doesn't mind how you do it.