Your description of the pilot light situation sounds perfectly normal to me. The pilot flame would be a nearly invisible blue flame, the red bit is the tip of the thermocouple heated to normal glowing red hot temperature by the pilot flame.
If the oven is only hot when you attempt to bake something, I see two possibilities: (1) you have accidentally set the oven to "broil" or (2) the thermostat has failed in the burner-on position. The cure for the first is obvious; the cure for the second is thermostat replacement. Either way, there is nothing wrong with either the pilot light or the thermocouple. (BTW, the latter is a fail-safe, and if it needed replacement, you would get no heat at all.)