Regarding shew (past of show), the OED in particular states that: The spelling shew, prevalent in the 18th c. and not uncommon in the first half of the 19th c., is now obs.

Why did shew become show?

Perhaps an explanation is in order. The Old English verb scēawian belonged to the class in which stress alternated between ē and the following vowel, so that scéawian coexisted with sceáwian. One variant yielded shew (still common in British dialects), while the other became show.

Is it Shewn or shown?

The past tense of show is always showed: She showed me her photographs. The past participle may be either shown or showed in most circumstances: She has often shown me her photos or She has often showed me her photos, as you prefer.