You basically create an INARA account, link it to your FRONTIER account and it automatically transfers all your information, (ships/Cargo/mats etc.) or you can do manual imports of your logs. I also use ED Market Connector and it can be set to send data to INARA in real time as well. Your engineered components can be transferred between ships, (assuming they are in compatible slots) but you need to Transfer them out of one ship into storage then switch ships and Transfer them FROM Storage to the ship.

You don't have to go through all the blueprints to go up to mods, but you do have to step through the various grades in one particular mod to apply the next one. Your TOTAL access to grades of Mods is granted whenever you rank up with any one blueprint.