any 12v charger will top it up if it is just a little bit low - any smart charger can be connected to keep it topped up over a longer period
it will need a charger labelled to suit MF/AGM/Gel/VRLA to recover it from very flat - the CTEK will certainly be okay. Says so in the instructions - this leaflet describes the charging phase. Older charges don't do the "fixed current" first stage which this type of battery needs if very flat.
No idea about the BMW charger, depends on its age. Can't find the part no. on google.
So my Motobatt failed after just 3 years and I decided it was time to modernise. Unfortunatly Lithium Ion batteries which are sold as direct drop in replacements on my r1150GS (2003) seem to be very expensive. Looking at the cranking amps specified in the original battery I bought one of these Lithium-ion motorcycle battery JMT YTX14AH-BS from Ebay about £108 and fitted it in with the foam block supplied and a few big cable tie. I've not been far yet and it not been cold (May time) but have started the bike some 20 times now and all is working well - really much better than even a new lead acid battery I think.