You can use ArangoDB Foxx as the sole backend of your application, however it is important to keep the limitations of Foxx (compared to a general purpose JS environment like Node.js) in mind when doing this.
You mention encryption. While ArangoDB does support some cryptography (e.g. HMAC signing and PBKDF2 key derivation for passwords) the support is not as exhaustive and extensible as in Node.js. Also when using computationally expensive cryptography this will affect the performance of the database (because unlike Node.js Foxx is strictly synchronous and thus all operations should be considered blocking).
ArangoDB does not support role-based authentication out of the box but it is perfectly reasonable to implement it within ArangoDB using Foxx (just like you would implement it in Node.js, except you don't need to leave the database).
For sessions there are generally two possible approaches: you can either use a collection with session documents (using ArangoDB as your session backend) or you can keep your services stateless by using signed tokens (Foxx comes with JWT support out of the box).
Complex/stored queries and input validation (using the joi schema library originally written for hapi) are actually some of the main use cases of Foxx so those shouldn't be any problem whatsoever.
Foxx comes with its own mechanism for queueing tasks, which can also be scheduled ahead or recur periodically. However depending on your requirements an external job or message queue may be a better fit. The good thing is you can get started with the built-in job queue right away and still move on to a dedicated solution if the need arises during development.
As for middleware and NPM packages: Foxx is not fully compatible with Node.js code. While we provide a lot of compatibility code and try to keep the core modules compatible where possible, a big difference is that Node.js is generally used to perform asynchronous operations while in ArangoDB all operations are synchronous.
If you have Node.js modules that don't use crypto, file or network I/O and don't use asynchronous APIs (e.g. setTimeout, promises) they may be compatible with Foxx. A lot of utility libraries like lodash work with no problems at all. Even if you find that a module doesn't work it may be possible to write an adapter for it like we have done with mocha (integrated into Foxx) and GraphQL (via the graphql-sync package on NPM).
In my experience it is a good approach to put your Foxx service behind a thin layer of Node.js (e.g. a simple express application that mostly just proxies to your Foxx API) and/or to delegate some parts of your backend to standalone Node.js microservices (e.g. integration with non-HTTP services like e-mail or LDAP) which can be integrated in Foxx via HTTP.
One more thing: while a lot of existing express middleware likely isn't compatible with Foxx because of Node-specific dependencies and async logic, ArangoDB 3 will bring a new version of Foxx with support for middleware using a functionally express-compatible API.