Gunnar Myrhe answered me yesterday night.
He wrote about the typo:
>"First, you have correct regarding the formula in the Supplementary Material of Chapter 8 AR5. The publisher introduced the unfortunate error in the final production of the Supplementary. An Errata was published soon after the publication, and can be found here:"

About the missing spectra:
>"It is also correct that the CH4 formula for CH4 includes only absorption bands in the infrared
part of the spectrum. "

He was though not concerned about the UV lines which I had pointed out to him:

>" Thank you for pointing to the UV absorption by CH4. The absorption is occurring at very short wavelengths and would therefore only be of relevance at very high altitudes . At these altitudes the abundance of CH4 is very low due to other sinks. I think therefore this UV absorption would be of very small importance. A solar absorption in the upper atmosphere would lead to a negative radiative forcing since less solar energy would be available for the troposphere-surface system important for the surface temperature."

And indeed I meanwhile found lecture notes which deal with this questions here:

>At 10 km (top of the troposphere) virtually all radiation below 290 nm has been absorbed. All radiation below 100 nm is absorbed in the thermosphere above 100 km. O2 absorbs strongly at wavelengths between 100 and 200 nm and also in a weaker band between 200 and 245 nm. O2 absorptions attenuate incoming UV radiation of less than 200 nm above an altitude of 50 km. Light of wavelengths of between 200 and 300 nm is strongly absorbed in the stratosphere by ozone (O3) and transmission of radiation of wavelengths less than 290 nm is negligible below 10 km. Between 300 and 800 nm the stratosphere is only weakly absorbing and most of the solar radiation at these wavelengths is transmitted into the troposphere. There is little tropospheric absorption below 600 nm but H2O and CO2, at high tropospheric concentrations, deplete the near IR part of the incoming solar flux appreciably. Hence, surface solar irradiance is dominated by visible wavelengths.

About the near infrared he wrote:

>"Near-infrared absorption by CH4 has been investigated earlier and I know it is under further investigations. It is not obvious whether the near-infrared absorption leads to a positive or negative forcing, since it depends if the absorption occur in the troposphere or stratosphere. "

I currently try to find out more about possible other UV lines which might not have been included in the MAINZ spectral data.