Re: how do you delete conversations in gmail?
You are using Gmail's Basic HTML View which, as you note, doesn't employ the cog button but instead has the far more JAWS friendly settings link. Here's a link to a Gmail help page on Using Gmail in Basic HTML View.
Your e-mail should already be automatically set up in Conversation View within the Basic HTML View. I just switched over one of my accounts to that view and conversation threads, the grouping of all e-mail messages with the same subject (or a reply with that same subject), are kept together as a unit and, when they're opened, the most recent message is always displayed and older ones will be if you haven't read them.
If I use the Delete button while reading a conversation it wipes out all e-mail messages related to the conversation. I can also do the same thing on the inbox screen by setting the checkbox (or checkboxes if you want to do more than one message or conversation) to checked and then hit the Delete button at the top of the message list.
I doubt that this Delete button is really a button (but not having JAWS at the moment I can't be certain) but it's visually presented as one. It could be a link.
This is how one conventionally deletes conversations or individual messages and I can't imagine it wouldn't work the same for you.
All of the above being said, it's now unclear to me whether you're talking about the inclusion of all prior messages in a conversation showing up in a single e-mail when someone responds to it, which is the default behavior. If what you're looking to do is to avoid having all the prior message text included in a response, with your latest addition at the top, but instead have only your addition be sent out, there is a checkbox beneath the Quick Reply text box where you compose your response that's labeled, "Include quoted text with reply," that is checked by default. If you uncheck this before hitting Send the only thing that will go out on that e-mail is the new material you've just composed.
If this hasn't answered your questions respond back.