Does anyone know are there limits for the speech recognition in iOS 10 (per device or per app)?
Yes, there are limits, but I don't think Apple has issued many specific numbers. Apple released a supplementary video during WWDC 2016 which said the following:
Now just a quick talk about some best practices. We're making speech recognition available for free to all apps but we do have some reasonable limits in place so that the service remains available to everyone. Individual devices may be limited in the amount of recognitions that can be performed per day.
Apps may also be throttled globally on a request per day basis. Like other service backed APIs, for example CLGO Coder, be prepared to handle network and rate limiting failures. If you find that you're routinely hitting your throttling limits, please let us know.
It's also important to be aware that speech recognition can have a high cost in terms of battery drain and network traffic.
For iOS 10 we're starting with a strict audio duration limit of about one minute which is similar to that of keyboard dictation.
Note the "let us know" part – Apple obviously want developers to use this new API, so if you find it doesn't do what you want they might be able to help.
As per Apple Latest Technical Q & A
The current rate limit for the number of SFSpeechRecognitionRequest calls a device can make is 1000 requests per hour. Please note this limit is on the number of requests that a device can make and is not tied to the application making it. This is regardless of the length of audio associated with the request. For a given SFSpeechRecognitionRequest, you are allowed up to one minute of audio per request.
Link to latest Apple Technical Q & A!