The large text fields allows you to use a limited amount of HTML, but you cannot change the Podio user interface as such. Generally speaking it's usually best to use more fields instead of cramming more stuff into one field. This makes it easier to work with the data later. E.g. instead of adding some HTML into a large text field that has some text and a link to an external system it will be better to have the text in one field and the link in its own field.
For the scenario you describe in 2): You cannot add buttons to the Podio user interface, but you still have options. The simplest is to use a link field or small text field to add a link to your external system. People can then click the link to do whatever you want.