Is it obligatory to wash the entire penis after transparent drops – possibly pre-seminal fluid (madhy) – are discharged following urination, and is this related to lower back pain? And is it obligatory to wash the penis if no pre-seminal fluid (madhy) is discharged before performing ablution (wudu')?

It appears that the drops that exit after urinating are al-wadi, and it is only necessary to wash the area of impurity, not the entire male organ. Istinja' (washing after relieving oneself) is prescribed to remove impure excretions. If nothing that necessitates istinja' has exited, then it is not prescribed to perform it before ablution.