The internal string limit in V8 (the JavaScript engine used by ArangoDB) is around 256 MB in the V8 version used by ArangoDB. Thus 256 MB will be the absolute maximum string length that can be used from JavaScript code that's executed in ArangoDB.
Regarding maximum URL lengths as mentioned above: URLs should get too long because very long URLs may not be too portable across browsers. I think in practice several browser will enforce some URL max length limits of around 64 K, so URLs should definitely not get longer than this value. I would recommend using much shorter URLs though and passing hugh payloads in the HTTP request body instead. This also means you may need to change from HTTP GET to HTTP POST or HTTP PUT, but its at least portable.
Finally regarding the HTTP response header "Server: ArangoDB"
that is sent by ArangoDB in every HTTP response: starting with ArangoDB 2.8, there is an option to turn this off: --server.hide-product-header true
. This option is not available in the stable 2.7 branch yet.