What to see/do and how to get around?

Driving on narrow country lanes is absolutely fine as long as a) you're happy to drive on the left b) you're happy with a stick shift (most UK rental cars are manual...if you want an automatic make sure you book long in advance) and c) you are sensible and take your time. Drive defensively and expect the unexpected (a slow-moving tractor, a herd of cows, a large milk tanker......).

Parking on narrow lanes is not a good idea at all. Don't do it. You'll often find lay-bys (pull-ins) and that is what you should use. Never park in farm gateways. 

Cornwall & Devon are both very big counties and both Guernsey & Jerseyare large islands. All have lots of 'musts' but you don't give any idea of your interests so I'm going to assume they include historical sites & sights? So, off the top of my head:

Cornwall: Tintagel Castle, Dartmoor National Park, Eden Project, Saint Michael's Mount, some of the many prehistoric sites (e.g. Lanyon Quoit, Chysauster Ancient Village), MouseholeSennen Cove, The Lost Gardens of Heligan, Lands End Visitors Centre (not the tacky stuff, the actual place) ...and lots more......

Devon: the wonderful Medieval cathedral in Exeter, Exmoor National Park, Dunster, Plymouth (England), Cockington Village,Kents Cavern Prehistoric Caves.........and lots more..........

Guernsey: wonderful lanes for long walks, Castle Cornet, the German Military Underground Hospital, the prehistoric tombs, Conway towers and lovely coastline of L'Ancresse, La Gran'mère du Chimquière, a unique prehistoric carving at Vale church...and lots more.......

Jersey: slightly busier with traffic than Guernsey but still with many lovely lanes for walking. Elizabeth Castle in Saint Helier, the amazing prehistoric (and later) site of La Hougue Bie, the fascinating Jersey War Tunnels, Mont Orgueil Castle in Gorey , the vast sandy beach running from La Corbière to L'Étacq, the vast sandy beach running from Saint Aubin to Saint Helier...and lots more....

Both Guernsey and Jersey have excellent bus services so you don't need to hire a car in order to see all the places I've listed (and more). It is unlikely that you'll be able to take a hire car from the United Kingdom mainland to the Channel Islands (which, by the way, are not in the UK) without paying a substantial premium, if you are allowed to do so at all. 

You're spoiled for choice, I'm afraid. Enjoy your planning! :-)