Why is the butter gradually melting and only the top of my butter cake done?
Your problem is baking on grill mode. Or at least one of your problems. Grill mode is designed to brown the top while not cooking the rest too much. As well as burning the top this may have the side effect of spoiling the rise of the rest of the cake, but still getting it hot enough to melt the butter.

In general for baking it's important to use a mode that delivers even heat.  This is typically described as "convection"/"fan-forced convection", simply "oven" or some similar term.  Modes like "grill" or "top heat" cook some things acceptably, and are often used for finishing foods that are cooked through but need a little browning on top.  Baking is one time when preheating the oven is particularly important even on modern ovens -- set the desired temperature and a light will come on.  It will go off when the oven is up to temperature.  You may wish to wait a little longer at this point.