Regarding the flame not igniting. The ignition process is the inducer starts first. A vacuum sensor verifies the inducer fan is working properly and then the HSI will be powered, the gas valve will open and the gas ignite. A flame sensor monitors the gas flame and if there is no gas flame, the entire furnace is shut down.
The flame sensor is a rod that has a voltage applied for the purpose of creating a current flow through the actual flame. A gas flame will conduct electricity. The control board monitors the current flow and if the current is not adequate, because there is no flame, then the furnace is shut down.
The causes for an inadequate current flow can be a dirty sensor rod (clean with steel wool or emery cloth), improper positioning relative to the the flame and the burner (the current has to flow from the rod, thru the flame to the burner or other grounded metal surface of the furnace), or a poorly grounded furnace frame (check all 120 volt wiring back to the main circuit breaker box for good connections).
In your situation you can try and get the flame to stay lit. However the blower issue seems to indicate a bad control board. The part you replaced ( L200F-30) had nothing to do with the fan... it's a high limit safety to keep the furnace from overheating. Usually the fan switching is through a relay on the control board. All the issues you seem to have could all be explained by a flaky control board.