Hi team! Harvester make it's host file-system read-only. If I change it will it be a problem?

You can't/shouldn't ordinarily change this as Harvester's OS runs from immutable images. What do you need to achieve that requires a RW root filesystem?

I want to install some tools using zypper

can you do what you need using a toolbox container? that's our recommended approach for this (see https://harvesterhci.io/kb/package_your_own_toolbox_image/)

Thanks! This is exactly what I need