Is it possible to do backpacking through Europe for 15 days with 1000USD? [closed]

This is the situation, I hope you can give me a hand:

On October 10th of this year I have an academic trip to Paris, it will take place from that date until October 22th. The trip is completely paid by my University, including tickets from my country (Colombia) to France, hotels, food and transport.

Now, It was proposed to me to stay some additional days if I want to, but the condition is that I must pay those days by myself.

This is what I've considered so far:

Time: I can not stay for more than 16 days starting from 22-oct since I'm in an active academic semester; more precisely, I can stay at most until November 7th (keep in mind this is only a time limitation and it's not related to budget or other type of limitations)

Budget: This is the hard thing. This opportunity got me with not so much money and I think I can only get about 1000 USD for the additional days (my local currency is very cheap compared to Euros and, it doesn't matter how much money I save here, in Europe, it will be only seen as one third of it).

The following is what I've planned based on other's opinions, travelers blogs and maps, among other resources.

The global plan: My initial idea is to travel Belgium, Netherlands, Germany, Czech Republic, Austria, Italy, Switzerland and go back to Paris given that my return flight leaves from there (Yeah, I know it, it's a very long trip with a very adjusted budget and time, that's why I need some help).

The specifically plan: I finish my academical things in Paris on October 22th, but I have paid accommodation until October 23th. My idea is to leave that day and head to Belgium, where I want to visit Bruges, then Amsterdam - Netherlands. In that moment, I'll head to Prague, crossing the German territory. After that, I'll go down through Austria to Venice, then Milan and then I'll return to Paris crossing Switzerland.

How am I planning to achieve it: The first thing is that I'm planning to have and adventure, I'm not afraid (I know I must and in some sense, I like it) of having austere conditions or being limited. I plan to travel by hitchhicking, I've traveled my country by that mean and I've read it's even more feasible on Europe (I need some advices about this item!), however, I'm sure I'll need to make use of some public transport in order to get out from some cities or stuff like that.

About the nights, I had in mind three things: The first one is to use CouchSurfing, I've never used it and I have an account on it with no references so that's probably an issue, however, I'll give a try and see how does it go (any advice with this? how should I ask? what should I add to the basic information?). The other option was to camp, I've never been out of my country and I don't know what temperature should I expect and probably this is not a feasible option, but it's present anyway. The last one is to use hostels, I've booked some prices and they seem feasible but half of my budget would be spent on accommodation if I sleep that way all days.

I can buy my own ingredients and cook, provided I have a kitchen.

Additional info: I must add that my plan is not to visit "famous cities" or "touristic places", I'm a lover of nature, landscapes, small villages and towns so that's something to keep in mind (however, Amsterdam, Bruges, Venice, Praga, all of them are touristic places! but they're not the priority, for example, I'm not planning to sleep on those sites or stay for much time). Also, I'm a man and I'm 21, if that's useful.

Well, those are all of my thoughts, this is a very important thing for me and I really hope you will help me, I'm on Math Stack Exchange and I know the friendliness and will of help of this community.

All the info I've gained comes from blogs and that kind of things, I've never asked someone personally or asked on forums, this is the first time.

Please give me your advices, recommendations and opinions, with no fear, if you tell me You're dreaming, that's impossible and give me good arguments, I'll take it at the best way. Also, I can change the plan, of course, I hear suggestions about other possible routes (maybe smaller) and other kind of things to do.

Thanks in advance!

EDIT: My budget is precisely 3'000.000 COP, USD is a little bit expensive these days so the convertion gives about 1.000 USD, but it can be a little bit more.