4. I read in a guide book, that you can get onto the local inter-city busses and ask to be dropped off at any spot in the middle. Is this true? If so, can you also 'hop on' to another bus afterwards?
The Regular Belizean buses stop for passengers anywhere along the route.
Express buses stop only at cities and main towns.
Since buses operate in 3 main zones (Northern, Western and Southern), transfers are done at bus terminals in Belize City, and Belmopan.
Alternate Adventures is a good company to deal with and their bikes are less than one year old. I would only rent the bike for the two days you are touring at the parks then take a bus to San Ignacio, eliminating the need to back track to Hopkins to return the bike. You can save considerable time by taking a plane to Dangriga from the municipal airport when you arrive in Belize City from Cancun
Better to plan your trip around Belize after you arrive. Caracol near San Ignacio is a great ruin to see, much better than Lamanai, however, the trip back and forth from San Ignacio is a total of 5 hours. I suggest hiking at Billy Barquidier National Park, it's relatively new, with a pleasant hiking trail and waterfall. It's between Belmopan and Hopkins. If you prefer hiking and photographing at a place more adventurous, where not many tourists have been to, I suggest Davis Falls. It has a spectacular waterfall and surrounded by large pools. I, myself, live near Billy Barquidier and Davis Falls. The Belize Zoo is also worth visiting, as my uncle-in-law donated the first jaguar to the Zoo, his pet named Pinto.