- people who obviously speak another language and whose
writing does not make sense
Not your fault if they didn't communicate intelligibly. I would go with stock "thank you for reaching out!" response. If it comes to it, it is entirely fair to say "I couldn't understand that last paragraph."
- Requests that are kind but have nothing to do with the product
Embrace them internally if they are useful. Acknowledge the effort put forward by the sender. try to engage if you see a path forward.
- Responses to people who make inquiries that really sound horrible
I'm not sure you what you mean, but there's no reason to take people's poor attitude. If someone crosses the line you have a duty to separate yourself and your organization from them.
- other things that may come up
Be polite, be engaging. Acknowledge people and be appreciative of their time and efforts. They took the time out of their day to give you something for free (ideas, feedback.) They may be happy to give you more of that if you ask for further details. Bottom line: people who engage you want to know that their efforts are well received, so as long as they are coherent and respectful, show them appreciation and don't be afraid to engage them in the ways that make sense to you (ask for further feedback, invite them to buy a product, etc.)
On the customer support end, if they are complaining about the product do your best to hear them out and satisfy them, but also be aware that some people cannot be satisfied.