Running a customized cron task very often
Is it overkill to run drupal cron so frequently ?


The answer to that is...it depends. If your cron task needs to run every 10 minutes, then no, it's not overkill. If it doesn't, then it is overkill. What you probably need is something like Elysia Cron, which lets you schedule cron jobs for specific modules on a an individual basis. That way you can run your custom labour-intense function as often as you need to without invoking the rest of the system's cron hooks.


  What are the main tasks that drupal cron is executing ?


There's a list of core hooks that will be invoked on a cron run here, I don't think listing each one of those here would be prudent (there are 16 of them) - suffice say to say quite a lot happens; the caches are flushed which is probably a point of interest.

Bear in mind that many contrib modules also implement hook_cron(), so if you want an exhaustive list of functions that are invoked on cron you'll need to go through those files manually.


  I understand that every task run within cron must check the last time it was executed so it is not run too frequently,


The must part of that is not true, there's no 'rule' for whether a task run on cron needs to check its last run time. There are plenty of situations where such a mechanism would be advantageous, but you absolutely don't need to do it. Again it depends on what each task is actually doing.