Unfortunately so unless you opt to use the Gamecube controller. The US version does not include support for the Classic Controller, however the Japanese version supports all three (Wiimote/GC/CC). I heard online that the PAL release also had CC support but I don't know that for a fact.
A bit, but not as much as the PS2 version and nowhere near the shitty PS4 re-release of the PS2 version. The individual Neo-Geo Virtual Console releases blow all the US produced SNK compilations out of the water, but for a casual fan the price of purchasing them individually might make Anthology a bit more appealing. The developer of them was quite shit (Terminal Reality) and their PS2 emulator chugs, while the added horsepower of the Wii runs a bit better. All the compilations they made run better on the Wii than the PS2.
To me, the main appeal of Samurai Shodown Anthology and Metal Slug Anthology (regardless of platform) were Metal Slug 6 And Samurai Shodown VI. Homebrew Neo-Geo emulation for the PSP and Wii are much, much better alternatives to playing the first entries, but these two anthologies are the only way to play these short of owning an Atomiswave board. I really like Samurai Shodown VI and play it on my Wii U quite often.