Hi there a07 - firstly keep your spirits up - I believe you learn nothing from easy projects, and this one sounds like the University of Delivery! Some perspectives from my experience....(and my first project as a junior manager was especially difficult!)
Even though the responsibility might lie with the Partner who sold this project, I believe the problem is sitting with you (right or not). As you're in a stretch role, out of your comfort zone and (to avoid a third cliche) really doing something that is not in your natural skill set - then you need to bear in mind a few fundamentals which any project manager needs to know (which I learned from some of my mentors in my early career)
1. Change will kill you if it's not managed. Fixed price = fixed scope Read the contract and understand the scope of your delivery. Read the obligations on the client side, the timeframes to deliver. Manage change to the micro-detail. Put in place a process to review, prioritize, review and re-estimate any changes before modifying any planning.
2. Get the people and the team right. Make sure you have a technical lead who is properly estimating, ordering and planning the development activities for the developers. Assign a functional lead who is leading the product testing - have them both report to you and keep the circle of discussion small and focused. If you have someone who does not fit the bill in terms of skills or attitude, get rid of them as fast as possible and replace them with someone who can step up to the role. For yourself, play to your skills of governance, workstream PM and use those skills to get the project management tied down better than ever before.
3. Manage upwards as well as downwards. You may need to step up and take more autonomy since you are being managed remotely your boss (I'm unclear whether it's the partner who is the boss or whether they are two separate people). Remote management by someone who is not fully dedicated will only be a disaster. Take the initiative here and start to insist on staffing and organizing the team according to your instincts and what you believe will work. Give your boss a weekly update and "filter" (ahem) his requests. The more experienced you get, the more you will learn to tune out the white noise coming from above and focus upon what's really important in it all. To be honest I think he'll be overjoyed that he has less remote work to do.
4. You don't say whether you're also accountable for the CCi% on the project - if you are, then my advice is that it's better to stop, take account of the situation, get your foundations solid and then proceed (even with the hit on the CCi) then to proceed on a shaky basis and make a loss. You're going to take a hit either way - make sure you come out of it making a profit.
These are typical factors you need to bear in mind - then keep the usual focus upon quality and communication - upwards, downwards, to the client.
I won't be as cynical as I could be on this topic (given your level) - but I hope the above is at least some good guidance which might help you out.
Keep positive, learn and don't walk away just yet!