Hi Jake..... Yes you can build your home into that south facing hill..... your soil looks like it has a lot of gravel (small rocks) in it... so it
should drain well. If you are NOT in an area that gets a lot of winter sunshine..... then having passive solar heat collection will not be of much help... because it depends on the sun shining in from the south (at a low winter angle) and warming a large mass that holds heat. Most passive solar heating setups require lots of windows (glass) on the south side of the house..... and if MOST of your winter days are cloudy and grey then you would actually loose a lot of heat ..... through all that glass.
About berming into the hillside..... I have built many barns, greenhouses and hobbit homes, dug into hillsides or bermed.... I always do a cement block (with rebar driven into the ground, coming up through the holes in the blocks, and filled with cement)... or a mortared stone wall or poured concrete wall with rebar or heavy wire mesh..... this is to hold back the soil when it is totally saturated with water and wants to move downhill. It is important to put a good French drain (perforated pipe at least 4" dia, surrounded with gravel, UPHILL, at the base of the retaining wall..... before you back fill it with dirt... If I am doing this in a rainy climate (more than 24" annual precipitation), I put a waterproof membrane (
pond liner) against the wall on the uphill side, curving it under the French drain and then back fill with the gravel (around drain) and dirt to the top of the wall.... I have built an
underground Mandan Indian Earth Lodge.... in rainy western Oregon, this way...... and there were often small streams of water flowing out of the down hill end of the French drain tubes.....during heavy rains.....
Be sure to find out how many average days of winter sunshine you get there.... you need at least 20 days of sun out of every 30...... if it is mostly cloudy... then you could mortar stone all around your
wood stove (except the door and the flat cooking top).... or you could build a stone wall behind your stove and put the stove right up against it............ thus the stones absorb all the heat and slowly release it during the night.... this is also a form of passive, massive heating...... We live in the southwest with over 300 days of sunshine a year..... most of the rain 24", in the summer as monsoons...... and we have an adobe (clay, sand & finely chopped
straw) Floor..... it hold the heat nicely..... and we have a stone wall behind the
wood cook stove..... all of this helps hold heat.... that is released at night... I hope this is helpful for you... best of everything to your family, Sunny