More seriously. I have done more or less what you plan three times I think.
Mull, generally great. Do a full lap if you can taking in as much of the western peninsulars as you can. If camping try Fidden Farm near Fionport. One of the best ever location-wise. Or semi- wild camp at Calgary bay which is worth a stop regardless.
Barra. You can lap it in half an hour. Visit the airport. Beaches and stuff via the peninsular to Vattersay. The most westerly road in Great Britain is there too.
Eriskay. You will probably scoot across it in two minutes from the ferry.
South Uist. Can be very very windy. West coast is wild and windswept with enormous long beaches. The “Machair” (dunes/lochs/rivers) just inland is unique to the area and well worth a mooch about. If you are a fisherman take, beg borrow or steal a rod. There’s some tracks along the coast you can just about get a bike along. They can be Sandy and you may get stuck. Damhik.
North Uist. It’s just a causeway to get on to it. I found it a bit scruffy. Best spot was to ride up to the mod radar /radio station for the views. I could see St Kilda.
Harris. Best island by far. East coast road is tortuous but spectacular. It takes 2-3x as long on that road compared to the main road. West coast has beaches like you have never seen. Tarbert - tweed, distillery and more. Hang a left about 1mile north and follow the road to the end at Hushishnish. Great beach and wild camping options. Even better beachrs an hour two walk away across the moors.
Lewis. More spectacular sea views and beaches. Black huts, standing stones,Butt of Lewis lighthouse at the north end is worth the ride up. Otherwise quite bleak and after the great sights on Harris a bit disappointing.
Skye. Fab place. A trip of its own really. Too much to mention really. Just ride around. You will work it out. Camping at Glenbrittle and a visit to the Fairy pools is on a long dead end road but well worth it. Seafood shack out the back of Colbost where Talisker is distillery (worth a tour) is worth a visit. Bunkhouse or B&b at Old Inn is ok.
On your other request for tips: boat the crew will either tie your bike down or give you the ratchet strap for a diy job - they’ll check anyway. Probably just over the seat. Use gloves or something to protect.
Camp or B&B. Do both. If the weather is shite b&b or hostel. If not camp.
Fuel, ummm it’s the uk and they have cars there. Lewis on a Sunday maybe difficult but generally every place of a half decent size has a pump. I think there’s a Tesco in Stornaway with fuel Station.
Weather.... you could have four seasons in one day, or four consecutive seasons in four consecutive days. Plan for wind and rain as that’s more likely than dry weather.
Here’s some links to places I’ve used
https://coolcamping.com/campsites/uk/scotland/scottish-isles/isle-of-mull/1083-fidden-farm
https://www.dunardhostel.co.uk/
http://www.gatliff.org.uk/
https://www.southuisthostel.co.uk/
https://lickistoblackhousecamping.co.uk/
https://www.dunvegancastle.com/glenbrittle/campsite/
https://www.theoysterman.co.uk/
Good hostel here
http://flodigarry-hostel.scot/