Elaina,
Exactly, I traveled the highway through a mix of buses and hitching. I used buses for the long distances: you can travel from Hualian to Taizhong in two days on public buses along this route (there aren't very many buses a day, so you're forced to spend at least one night in the mountains if you stick to public buses). I hitched a few shorter rides up in the mountains; I found hitching very easy, and had offers of rides all the way through the mountains. I found places to stay simply by turning up to villages and asking around. I also had a tent with me, and camped a few nights, though mostly off the main highway. If you do go, you need to plan a little carefully: there aren't that many villages along this route, particularly on the Hualian side, and consequently the distance between places to stay is sometimes quite significant.
I have been to Lanyu, I spent 4 or 5 days there. I think the most interesting thing about the island is the people - in terms of how they look, how they behave, and how they speak, they are very different from the Chinese-dominated culture on Taiwan. There's quite a unique culture here - unique at least within Taiwan - and it's very interesting to see. Some of the younger people on the island can speak English (my Mandarin wasn't very good when I was in Taiwan, though Mandarin is as much a foreign language on the island as English is) and I had some lovely chats with people getting to know what life on the island is like. The island has six villages: the three villages on the western side are a little more modern. The other three - two on the eastern side, one village called Lantou on the north - are more traditional, with traditional half-underground houses still being lived in. I stayed in a lovely homestay - the home stay had no name, but the woman of the house suggested it might be called the "Surfboard Guesthouse" since there were a couple of surfboards hanging around in front of the home. In summer at least, the island is popular with young Taiwanese (the island only has 3 or 4 buses on it, which thankfully limits the number of tour groups) and there are a lot of homestays. The three villages round the back of the island remain mostly local villages however, and have a nice feel to them.
Apart from that, the island is gorgeous. It's basically a volcano in the middle of the sea. You can bicycle all the way around the island in about 2 hours, and there are several places where you can climb up the forest-covered interior. You can also swim and snorkel on several volcanic beaches. The boat ride to the island is about 3 hours if it's direct; some of the boats stop at Green Island, which means the trip will last longer. I traveled to the island to and from Taidong. Most visitors to the island rent scooters, which are available at the dock. Alternatively, you can get a bicycle: close to the dock is the island's rudimentary government office. Outside the office is a large pile of unlocked bicycles, and you can choose whichever one you want and ride off on it, provided you leave it back there before you leave the island! The island has one main ring road of about 35km, and one cross-island road in the middle. The cross-island road is very steep, and you'll probably want to walk your bicycle up and down it.