So let's get some things out of the way first. I'm 17 years old, currently studying Communication & Multimedia Design (first year) in Rotterdam, the Netherlands and together with a friend of mine we decided to tackle a (design) problem. We aim to provide a solution to this problem through a platform and are currently in the concept development stage. We are both very exited about the idea, yet very cautious not to tell anyone what we're working on because we don't want anyone to run away with our idea of course. So the burning question remains, when is the right time to launch the idea? We have already done user research, analyzed it, defined the problem, developed several ideas to solve that problem and chose one to work out. We are currently working on a clickable prototype, promotional video and a website. Before we launch the website and video we aim to test our prototype (mainly on usability). Is this the right time to launch the idea?
You've been doing all the right things, so you're on the right track. Not sure what you mean by, "launch the idea" though. You can't start selling it until you have an MVP (Minimum viable product), and it doesn't sound like you do.
Your next steps are to make an MVP and deploy it to people with the appropriate personas you identified in your previous user research. Your MVP, and defined personas will most likely be iterated as you do subsequent testing, that's normal.
In order to get people to test out your MVP you don't necessarily need a website or promotional video, but they may help in the recruitment of testers if needed. Nobody other than the people you solicit as testers are going to see the website, so don't worry about that. You don't have to be very secretive, but if you want to be cautious, you can ask if anyone wants to test your MVP (on forums, etc.), and describe it in general terms (i.e. just describe the problem it solves, and maybe generally how). Then for all the people that are interested you can give them the details and show them the device (or whatever it is) and see if they're still interested.
You should have all your solicited testers fill out pre- and post- questionnaires which will help you quantify optimal personas, the functionality of your product, approximate price people might pay for it, etc. I've done many of these myself, and also helped lots of other people design them, analyze the results, and iterate their MVP based on the results. Let me know if you'd like any help, or if you have any questions relative to the specifics of your product.
best of luck,