Customizing the dashboard – how?

I’m using WP as a CMS. So far so good.
Currently I have 15 contributors, and increasing. I would like to add my own applets to the dashboard.

So my question is:

1. Can I make my own applets / plugins and show them on the dashboard?
2. Can I use the screen options to add / remove these applets / plugins?

I’ve look at other posts, but non has any answers really (and most have non at all)
https://www.ads-software.com/support/topic/174612?replies=4
https://www.ads-software.com/support/topic/250976?replies=1
https://www.ads-software.com/support/topic/224159?replies=1