Read-only connector for Target system

Hi,

Just wanted to confirm few things regarding synchronization project.I wanted to configure a synchronization project that only reads from the target system and chose the option "read-only access to Target system" before finishing the configs.

However, under the mappings, I can see few objects whose properties directions are both ways and few are in the direction of the target system.

Just for my understanding, will the connector write back those properties back to the target system?

Is it necessary for me to edit all those property mapping rules, and edit the mapping directions?

Or should I go to Configurations > Target system > general tab, setup and choose the option "connection is read only"? Also, I was expecting this option to be checked as I had checked the read-only access while configuring the synchronization project.