How to conciliate REST and JSONschema?
If I understand you correctly, you want to use JSON Schema for input validation, but you are struggling to figure out how to validate query parameters with JSON Schema in a RESTful way.
Unfortunately, there isn't a definitive answer.  JSON Schema just wasn't designed for that.  Here are the options I have considered in my own work with REST and JSON Schema.

Convert query parameters to JSON then validate against the schema
Stuff your JSON into a query param and validate the value of that param.  (i.e.  /foo/1?params={"page": 2, "perPage": 10})
Use POST instead of GET and stick your fingers in your ears when people tell you you are doing REST wrong.  What do they know anyway.

I prefer option 1 because it is idiomatic HTTP.
Option 2 is probably the easiest to work with on the back-end, but it's dirty.  
Option 3 is mostly a joke, but in all seriousness, there is nothing in REST or HTTP that says a POST can only be used for creation.  In fact, it is the most flexible and versatile of the HTTP methods.  Think of it like a factory that does something.  That something could generate and store a new resource or just return it.  If you are finding that you need to send a large number of query parameters, it's probably not really a simple GET.  My rule of thumb is that if the result is inherently not cacheable, it's possible that a POST is more appropriate (or at least not inappropriate).
I'm starting a new project that consists in an Extjs 6 application with a pyramid/python backend.
Due to this architecture, the backend will only provide an RPC and won't serve any page directly. My implementation of such a thing is usually based on REST and will fit nicely this CRUD application.
Regarding data validation i would like to move from Colander/Peppercorn that i always found awkward to the simpler and more streamlined jsonschema.
The idea here would be to move all the parameters - minus the id contained in the url when is the case - of the various requests into a json body that could be easily handled by jsonschema.
The main problem here is that GET requests shouldn't have a body and i definitely want to put parameters in there (filters, pagination, etc).
There's probably some approach to REST or REST-like and JSONschema but i'm not able to find anything on the web.
Edit: someone mentioned the question about body in GET HTTP request. While putting a body in a GET HTTP request is somehow possible, it's in violation of part of HTTP 1.1 specification and therefore this is NOT the solution to this problem.