Silicon-based life on Alpha Centauri Bb?

This is an interesting question. The Si-Si bond is only about half as strong as the C-C bond, making Silicon life more fragile than Carbon based life. However, the Si-O-Si bond is enormously strong, so silicone life would be more likely in a hot environment. (Note that I said silicone rather than silicon).

It has been said that the siliceous magma on the Moon that filled up the Moon's maria basins had the consistency of motor oil. The siliceous magma ocean on Alpha Centauri Bb would likely be hotter and therefore even more fluid. The only impediment to life in my opinion would be the establishment of some sort of cell membrane in that environment. But if this were possible, allowing the life form to maintain "self" from "non-self", then I see no reason why silicone life not could exist. Multicellular life might even form, with solid quartz for bones. They could be eyeing our solar system for a "Venus-like" planet that they could warm up further and live on in the future, similar to our thoughts of warming up Mars. Earth would be worthless, too cold!

Your last statement is probably the most important. A big part of the habitable zone is related to the ability to keep certain compounds liquid so that they can act as a medium for chemical reactions.

Magma isn't likely to work. It won't act as a solvent, and the extreme temperature would limit what chemical reactions could take place anyway.

It might be possible but such life have precious little in common with us making communication extremely difficult, right now our priority should be the search for carbon based life forms that would be easier to recognise. The main reason we're looking for an Earth 2, is not so we can communicate but so we can eventually colonise, so the ideal situation would be a planet with an Oxygen Nitrogen atmosphere like Earth, plenty of fresh drinking water, vegitation that isn't poisonous and indigenous life with no measurable intelligence (i.e. non sentient animals).

The search for INTELLIGENT life that we can communicate with is being undertaken by SETI to date there have been no signs.

Silicon isn't capable of forming the wide range of complex molecules to anything like the same degree as carbon is. This doesn't make it impossible but it makes it much less likely.