I certainly agree they have a lot in common with classical theism. They certainly have more in common with it than any of these schools of thought have to do with much modern thought. It is probably the Aristotelian school that has least in common with much Eastern thought (although it must be remembered Indian thought is made up of far more than non-dualists - there are qualified non-dualist and followers of philosophies closer to mainstream Western theism). But Platonism, Sufism, Palamism, the schools of Suhrawardi and Mulla Sudra, for example, seem to have much in common with a lot of Eastern thought. Of course, there are many distinctions to be made, so I'm talking impossibly loosely.

In general, Eastern thought is not philosophy in the modern sense, but then neither is most pre-modern Western thought. With the exception of some Hellenistic schools, it is Scholasticism, especially in its later forms, that bears the least resemble to most Eastern thought, of all pre-modern Western schools. Buddhism is simply one of the most extreme examples of divergence. Buddhism is radically apophatic. Its philosophy is designed, ultimately, to break the hold of discursive reason and categories, and illuminate the intellectual intuition - Bodhi ​(बोधि). But even someone like Shankara is not involved in the same entreprise as a Bertrand Russell or, to some degree, even an Ockham or Duns Scotus. Though there is some resemble between Buddhism and ancient scepticism, Buddhism ultimately has a spiritual and intellectual purpose that seems missing from the what we know of the latter. The spiritual beliefs of Buddhism shouldn't simply be equated with any other position, but they bear resemblance to Platonism (I mean the Platonism of Plotinus and Proclus, not any definition used in modern philosophy) and forms of Christian and Islamic mysticism. Nirvana (although Buddhists are often loath to make positive statements, we as non-Buddhists can ignore that for our present purposes) is the absolute - as well as bliss, knowledge, permanance - and in much Mahayana thought holds a position similar to the non-dual thought of a Shankara or Plotinus (Samsara is Nirvana, as the saying goes). 

I don't think that is correct. Buddhism, especially Mahayana, makes extensive use of its own forms of logic and taxonomy of the elements of reality. This is held to be incomplete, but not illusionary. Buddhist logic is used to break the hold of discursive thought, but it does hsve it own role to play - to a degree it is held as important knowledge about reality.