1. No the devices you are wanting to monitor do not have to have IPMonitor installed. You only need that installed on the machine you want to monitor from. All the client machines/appliance/etc just need to be setup to use RPC/WMI or SNMP. For best results i would use SNMP, it uses less resources than RPC/WMI and is quicker in my opinion. For the credentials it is trying to use RPC/WMI and you will have to add a Credential that has permissions on each device you are wanting to monitor. You can add a credential by going to the CONFIGURATION tab and then select CREDENTIAL LIST to add some. Again you can use SNMP to monitor a lot of things but if you want to monitor Files/Folders/Logs/etc...you will have to add Credentials for those.
2. No it does not have to be open to record data. You do have to select the option for it to save hostorical data for each monitor though. If your install is not recording data even though the option is selected then you need to contact support because you should not need to leave the web interface up for that to happen.
3. Not sure about MACs as i dont monitor any but im guessing MACs can run SNMP in which case you could still monitor them.