From the Czech text, I am able to understand (I hope!) that the translation into English can be both, 1.They are trying.. 2. He is trying.. Though I have one question, even quite important. A regular request for strangers that visit your marvellous country, would sound like "CAN YOU TRY TO SPEAK SLOWLY?" But how is this request in correct Czech?? Is it Snažíš se mluvit pomalu?! or is there a better and more correct way? Waiting for your answer, thank you Vlada for all the help!
If you insist on the verb "try", you can say, maybe, "Snažte se mluvit pomalu" for plural or "Snaž se" for singular. But you can use it in a special context (e.g. if you are a speech therapist and you are teaching an ADHD kid). If you just want someone to talk to you slower because you cannot understand him/her, you would use the version of our mate here - rsail.