So prior to the Esperanto course release, I studies Esperanto through other means since January of this year, specifically a book about the workings of the language I downloaded on my phone (which I believe was written between the late 19th - early 20th centuries). Sections that the book went over in particular were participles which used the suffixes -anta/-inta/-onta.
Mi estas estanta... (I am being...) Li estis aminta (He had loved)
Now I have not completed the Esperanto tree as of now (though I am in the last section) so I do not know whether these will be discussed, but as of where I am, I have not seen even the slightest hint of these. This leads into my question- are participles in Esperanto rare, or are they not used at all?
They can be found in the Eduction section of the tree, this part in the notes section explains why there isn't much about them in the course:
This is an introduction to participles, which are important to recognize and start to learn, but which are not needed for most everyday interactions in Esperanto."
Go to books.google.com then Search for Esperanto, then on the top right hand corner click the gear icon and click Advanced search. From here change Search: to Full view only and click the Google Search button. That will give you a list of all free out-of-print public domain books that Google has scanned about Esperanto.
Simple alternatives for me by simple verbs and words: mi estas manĝanta (nun) = mi manĝas (nun); la pordo estas malfermita/ata (nun) = la pordo estas malferma (nun). La viro estas/is mortinta (jam) = la viro mortis (jam) aŭ la viro estas morta. Mi estos dormanta (baldaŭ) = mi dormos (baldaŭ) | Mi estas dormanto (baldaŭ) = Mi dormos (baldaŭ). Or prefer them alone: lernanto/a/e (nun), lerninto (jam), lernonto (baldaŭ). In esperanto conversation we don't need complicate like our languages.