I want to know if a VPN service is safe or not. If the VPN server itself can catch or sneak peek my data? Or as long as it is a VPN service, then the security is protected by the algorithm itself?
For example, if I use the VPN server to connect to Google services, is it possible for the VPN server to see my data (e.g. username & password of the gmail account)?
If any VPN servers cannot do so to steal clients' data, then I think I can trust any VPN servers. Otherwise, no.
I don't think you can. In theory VPN can be set up as full proxy, so all traffic can be inspected. This is setup setting and usually as a user you can't really "detect" if the VPN provider is doing this or not.
You shouldn't trust ANY VPN service provider.
They potentially could if you were using an unencrypted service, eg http, but most sites will use encryption (eg https) by default.
When you log into Google Services over VPN, sending data over the VPN encrypts it a 2nd time (using different keys ...) At the VPN provider they decipher the VPN encryption and then send out the only-once-encrypted packet to google services . Only google services can decrypt the 'inner' message.
It's up to you to make sure you're using encrypted services when you need to use a password... but that is true of all internet transactions not just VPNed ones!
Yes, the VPN provider could easily see the data you're sending over the VPN connection should they so choose to.
There are some steps you could take to at least see if the VPN service is requiring you to send all recursive lookups (DNS requests) for your web traffic through the tunnel or not. If you're on a windows host, you can do one of the following from an elevated command prompt:
netsh interface ip show route or route print
These will show you your routing tables on your local machine. When you connect to a VPN, the VPN will inject routes into your routing table for the VPN to work properly. Look for your wildcard route(s). They look like 0.0.0.0. These are there to direct all of your DNS lookups (which are used when requesting address information for an FQDN or domain name if you prefer) and if you have one pointing to an IP address listed other than your router or home IP router, then they are likely forwarding all of your DNS traffic through the VPN. In this case, they could theoretically see just about everything you're doing on the Internet.
As far as the potential malicious intent of the VPN provider, that's up for you to decide. The idea behind connecting to a VPN is to keep the badies out, not provide a direct connection to them.
You've got the wrong idea about VPNs. You don't get a VPN so that you don't have to trust anyone -- that's not possible. You get a VPN so that you can trust the VPN provider instead of whatever network you're directly connected to. Don't buy VPN service from someone you don't trust, but if you don't use a VPN then don't connect your computer to a network whose operator (including downstream operators) you don't trust. You have to trust someone.
