I assume that you are talking about the android status bar.
(a) When your cellphone is connected to a network, android tries to connect to a webpage to verify if internet is available. If the webpage is not reached, then an exclamation mark is shown, which may mean that you have a network connection, but you cannot reach external services.
(b) The meaning of H is the type of connection. G stands for GPRS, E for EDGE, H for HSDPA, H+ for HSUPA, and so on. They talk about the connection speed.
(c/d) If the triangles are blank or full depends on your connection signal. If your signal is strong, triangles are shown with full painting. If your signal is weak, triangles can be shown empty or something in the middle.