See Day 17 Vrikmasana for some notes on standing half lotus.
To get into half lotus : Bend the knee bringing it towards the chest, allow the knee to drop out to the side, key here is the natural rotation in the hip joint. Bring the foot close to the opposite thigh, hold your foot in one hand and the knee in the other and GENTLY encourage the roration of the ball and socket hip joint, bring the knee forward parallel with the floor towards the opposite knee and the foot further up the thigh and ideally, eventually, towards the groin.
You don't want to force this action, if you feel strain on your knee it may be better to practice tomorrows subroutine built around mama mudra with the foot against the thigh rather than on top instead. Practicing the maha mudra subroutine will bring half, and eventually, full lotus closer.
As we have found in all forward bending asana, stretch out of the hips as we practiced in the standing On your feet sequences, the same goes for the twisting postures.
In picture six (the raised hip), Vasishtasana or Kashyapasana we must be careful of the knee. Work from the top down, pushing down into the mat and lifting your shoulders then lifting the hip which will allow the leg to straighten, lower in reverse, DON'T push off the mat from the foot, knee or hip first as this will put too much strain on the knee which is vulnerable here.
The lift /Utpluthi (pic9)
Lean forward , put your hands slightly forward of your hips, engage mula and uddiyana bandha, drop your shoulders bend your elbows. Now push down through the mat lifting your body off the mat. At first you might only manage to lift your backside off the mat, your heels remaining grounded. However, keep engaging the legs for the full count of three to six breaths as this will build strength for future attempts.