YES you are right.
Load is CPU's V-CORE, current consumption MAX to 2A.
Because I am not much familiar with DCDC buck, so I don't know if the LX signal is fine or not.
No, the waveforms shown are quite normal.
The circuit shown is a Synchronous Rectifier type where the normal diode is replaced with Q2. Q2 would normally be on when Q1 is off.
The output ripple can be caused by a number of things.
Parasitic capacitance of the inductor windings. This allows the fast edges of the switching waveform to partially bypass L.
Poor ESR of Cout. Large electrolytic types will exhibit this. Several smaller value types will help to mitigate it. A few 100n ceramic caps will also help.
Poor layout will also contribute. One of the main candidates here would be poor grounding. All the high current points should sum at one junction and not be daisy chained.
A lot of the rubbish on the output could be removed by the use of a high impedance Cylindrical Ferrite core on the output leads.