I can answer for 3scale since I work there.
3scale is a complete API management platform that implements authorization, rate limiting and analytics for your API. We offer different integration options the most popular of which is our API gateway, that can be hosted by us or deployed on-premise.
This is an Nginx-based gateway that is deployed in front of your API servers and authorizes incoming calls by reaching to the 3scale API. The gateway extracts the API key of the incoming call and the endpoint that is being called and checks whether this particular request should be authorized (i.e. valid key, usage within limits, valid endpoint, etc).
One key part of our API gateway is that the authorization is performed asynchronously so that it has no impact on the latency perceived by the API user.
Regarding your particular questions:
We have 600 customers using 3scale in production. This includes APIs with very large traffic volumes, some of which you can see and read about here.
I'd say the main choice is between using an API management platform or implementing these features yourself. The advantage of using something like 3scale is that we specialize in exactly this problem and we provide other very useful features besides the basic authorization and rate limiting: a developer portal hosted by us where your API users can register and manage their keys, a billing system that you can use to offer paid plans for your API, support for advanced auth patterns like OAuth2 and others that you can read about in our website.
You could also integrate 3scale in your API with one of our software libraries. However since you have multiple APIs written in different languages I'd recommend the API gateway since you will only have a single integration point (therefore easier to maintain).
As always the best is if you test it by yourself. We have a free plan with no time limits, so you can start there.