You're very welcome, and thanks for checking out my site. :-)
Yes, arriving in Takamatsu in the evening will probably make your life easier.
1. The reason I'm advising you to spend more time on Ogijima than Megijima is because Ogijima is a much more interesting island. In all honesty, Megijima is mostly "Takamatsu Beach", but off season, there isn't really much to do or to see on the island (do not spend time and money going to the cave unless you have kids). On the other hand, Ogijima is probably the cutest island in the region, the village is simply beautiful, if you decide to walk around the island, you'll have a great experience of the Seto Inland Sea (OK, you can do that on Megi too). The people are super nice and welcoming. It is also the success story of the area in terms of island revitalization (population has grown steadily for the past three years, something unique in Japan) and all the young blood is bringing a great energy to the island (go check the library).
I can spend days on Ogijima (oh wait, I do... I go there once a month, at least), while a yearly trip to Megijima is more than enough.
And of course, there's the art (be careful, it's open only on week-ends on both islands), but even the art is more interesting on Ogijima than Megijima (Ogijima's Soul, Onba Factory, Memory Bottles, Akinorium and the Room inside of the Room are some of the best artworks of the whole area). On Megijima, the Island Theatre, MECON, the Presence of Absence and Equipoise are not to be missed.
So, my advice would be take the 10am ferry to Megijima, stay there until 12.20pm (two hours is enough time to visit the art, walk around the village and along the beach a little) and then stay on Ogijima for the rest of the day (visit the art, get lost in the village, hang out at the library and Onba Café, etc.)
2. Visiting Inujima and Teshima in one day is not very realistic. Inujima can be visited in two hours, but Teshima is closer to one day and a half. :-)
Now with that being said, I've done what you're planning: Inujima in the morning, then arriving to Teshima at 1.30ish and visit parts of the island for the rest of the day. If you limit your visit of Teshima to only on part of the island (let's say Karato, where the Art Museum and Shima Kitchen are) you can do it, and you can have an interesting experience. Just don't expect to visit all of the island. If you don't mind returning to Takamatsu late, when you're in Karato, instead of having to return to Ieura to catch the last boat to Takamatsu, you can take the ferry from Karato-hama to Shodoshima and then from Shodoshima to Takamatsu. The price won't be very different, but it'll take almost two hours instead of 35 minutes. However, it may allow you to visit more art on Teshima (you won't have to go Ieura-Karato-Ieura, just Ieura and then Karato).
3. You mean Umiyado? I never ate there, but I heard very good things, and the owners are very nice. However, if you decide to follow my advice, you may not have the time to have lunch on Megijima. In that case, may I advise you to have lunch at the Library on Ogijima, or at Bistro Iori.
Once again, I hope that helps. And do not hesitate to ask more (just this forum doesn't send e-mail notification, so I may forget to check it out in a timely fashion - the other option is to contact privately from my website).