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Modem - you get what you are given, but that will normally be the 250.
Password protection of modem, not possible as far as I know. You should always have yoru own firewall and stuff. There is the free ntl netguard, but I prefer to rely on hardware and thus the firewall in my router.
Engineer should check everything is OK on installation, especially signal levels.
YOu have no choice but to go through proxys for port 80 web stuff.
Some ports on ntl are disabled - there's a list somewhere - mainly affects business type software such as M$ exchange
20:1 contention is the norm, and beats many ADSL services
Distance is less of a factor with cable than ADSL so speeds are more consistent, provided signal levels are in tolerance. Of course contention could be a factor (as it is on ADSL too) if there is a big leecher in your vicinity.