1. Going back to my desktop email client so that I can paste screenshots into outgoing emails. 

Any chance you could enhance your email client to that it supports inline paste, like http://snag.gy/

2. Forwarding an email that I've received on my personal account to the support@ address, only to have the ticket created for me, and then forgetting to update it, and having all the replies go to me and not the customer.

Any chance you could look at an email ticket, and if it's from someone who is already registered as a support agent, parse the content to find a more likely account to own it?

3. Cleaning up after a conversation where my customer has emailed an individual (and cc'd the support@ address), and the individual has replied from their main email client (and cc'd the support@ address), and the conversation has gone on and created dozens of tickets in Zoho, which I have to merge by hand, and I'm only allowed to merge 3 at a time.

Any chance you could let me bulk merge emails, and/or use internal email header properties such as Message-ID and In-Reply-To to automatically group emails into tickets?