Connecting development tool, bug tracking, test case management, and ticketing

I don't know if this is the right place to post this, or if that title makes any sense, but I would love some help 🙂

I started a SaaS company a couple years ago. Our team is growing – we now have me, a customer support rep, 6 developers, and a QA engineer who just started. I oversee everything. I started with no experience in product management / development and though I've come a long way, I still have infinity to learn.

As we have grown, our process has become an unruly mess which has led to bugs and slow progress. So, I recently wrote out a full SDLC, implemented a structured process for commits, pull requests, code reviews, and releases and have just started the process of adding in the QA component as well.

Where I'm mostly stuck is what to do with tools. Currently we use:

• Asana to manage tasks (A Kanban board with a flow from ideas through to deployment)
• Zendesk for ticketing and helpdesk (users submit through email, the ticketing system, or the platform itself)
• Currently in the search for the right test case management tool – considering TestRail. In all honesty, I have probably a 15% understanding of how the process of QA is actually supposed to work
• Slack for internal communication

In the connections between those things, everything is falling between the cracks:

• We copy requests manually from Zendesk to Asana but things get lost.
• We complete tasks in Asana and forget to update users in Zendesk.
• I love Asana for managing tasks, but we currently have >200 open requests/features/issues and when someone asks me how long it will be before task XYZ is done, I lay down and cry.
• I can't find a test case management system that doesn't look like it was built in 1995 for a 10,000 person Telecom company and I can't find something that will play nicely with Zendesk/Asana.

So, it's a bit freeform, but help!!! What flows and stacks have you worked with that have been successful? Any tips?