What is the correct position of the word 'also'?
I would like to also talk about ...
I would also like to talk about ...
It depends on what you want to say. Are you also liking or also talking? I.e. Are you trying to say that alongside liking something else, you would like to talk about ellipsis? Or alongside talking about something else, you would like to talk about ellipsis?
Also is an adverb, so it can go next to any of the verbs.
Number 7 is wrong in the context of wanting to talk about ellipsis. Number 6 is an unusual choice stylistically, I think it hints at a low confidence moment for the speaker, because the also is added in at the last possible moment.
Numbers 1 and 2 means that someone else is speaking about ellipsis and you have something to say as well, 2 has emphasis on I and possibly also.
Numbers 3 and 4 can mean this too, but they can also mean that as well as something else you are talking about you want to talk about ellipsis. 3 has emphasis on also like in the second context. 4 is more likely to be applied to the second context, to apply to the first context the emphasis would be on I and also.
Number 5 can only mean that as well as something else you are going to talk about ellipsis.