Rasritz,
As dwayneg has previously stated the Caller ID should show up with no issues so you may need to look at some flags for that depending on whether or not the user's endpoint is receiving Caller ID or not on any call types.
As for the MoH there may be some stuff you can look at to see if MoH is suppose to work on IC calls.
Go to System > Flags > Music-On-Hold for IC Calls: Yes
If that is already set to yes on both sides then you may need to look at whether or not both sides actually have a Music on Hold source to draw from. If they don't then you would be sending MoH audio across your network, which is not advised; although you can do it.
Under the Call Configuration for each node at each site there is a Node IP Connection Group that has the IP Configuration for that Node IP Connection under it. There is where you will find the Music on Hold Encoding Setting which by default is set to Use Local Music Source; this means whatever your local MoH source is. If you set this to Use Speech Encoding Setting then it will play whatever the remote site has for its MoH source.
Thanks,
TE