You can do all of that via Redstone basically, but there is no “direct” Compat with any Computer Mod.
As for the Logistics Core, yeah what would the Computer even do? I mean you can turn individual Imports/Exports/Storages ON/OFF using the Cover-Controller-Cover and Redstone, so that would be another thing. A lot of things have Redstone Compat as to make sure everything can interface with it on a common level.