1) This issue is very common, and hard to avoid unless you do a lot of research beforehand on what setup to get for which games.
May I ask what tv model and brand you have? It's almost assuredly your tv having 2-3 frames of input lag because hdtvs are not usually designed for competitive gaming. You won't notice it with other games (unless you play rhythm games) because very few of them require frame-perfect execution and immediate response times like smash.
2) CRT will not be standard for Smash4WiiU: a gaming monitor by ASUS or BenQ will be standard I'm sure. For comparison, a CRT has 0ms input lag (or 8.33 by Leo Bodnar standards), while a top gaming monitor has 1-2ms input lag (or 9-10 by LB).
This amounts to a difference between the two of about 6-12% of a frame by the way, and a 27" gaming monitor is about $320 these days for 1080p and 60hz refresh rate. It's the gold standard for competitive console gaming.
I'm looking into whether CRTs are still an option for tournaments because the Wii U might have a digital-to-analog conversion lag of about 1ms through the RCA port on the back meaning price is the main issue to switching from CRT to gaming monitors.
You're mostly correct but you have your numbers all wrong for the input lag part.
CRT has about 0ms, top gaming monitors (BenQ and ASUS) have about 9-11ms of lag.
Also playing this game competitively on an HDTV is not going to work... like at all lol...
With there being a digital to analog conversion lag, this isn't true either, because technically speaking all frames are rendered "digitally" and are either output as analog or digital. If there was a delay to this, we would see this in all game consoles when connected to CRT TVs.
PS. Pro-tip: CRTs have more lag if you're using Composite as opposed to S-Video or Component since there's more breakdown of the analog signal to the tube inside the TV. Whether or not you'll notice it is a completely different story.