[chryuop]

Just a suggestion. You are mixing two parts of grammar and that is why you might have a little bit of confusion. Look on your textbook this 2 separate topics and tackle them separatly:
transitive/intransitive verbs.
continuative/moment action verbs with the progressive ている form.

They should be in 2 clearly separated parts of the book. The different meanings with the ている form has really not much to do with how the transitive/intransitive verbs work. usually they are dealt with in different section of the book.

てある itself will be covered in another area of your textbook for sure since it is a form that can take the place of the passive form.

Try to learn them separately, that will help you alot. Trust me, lol coz we all students go through the same confusion when tackling these things LOL.