how safe it is to use this service?
Nothing in the world is safe to use, remember it. Even your bank accounts, credit cards, personal data, etc. are NOT safe, as they can be hacked. Argue against, if you don't agree...
How about the general server security?
This is not your headache. Your headache must be how to secure your login and password. For this purpose, your sat-receiver settings must be password protected to avoid hacking.
Which data is stored on the servers? Is the data encrypted?
You are too much curious about data stored on the servers. This is absolutely not your business which data is stored on the servers, as well as data encryption.
Data transmitted by satellite providers is encrypted (SURE). We decrypt it. How? This is our KNOW-HOW.
Any general advices when using this service?
Keep your receiver password protected, follow the server RULES and everything will be OK.