OP: why is the nidāna of jarā- maraṇa replaced by the more general term
dukkha in the concept of lokuttara paṭicca-samuppāda?
Suffering (stress) is a more general term while disease and death are specific forms of suffering.
This sutta uses the general form of dukkha, because that's the basis for connecting the lokiya paticcasamuppada to the lokuttara paticcasamuppada
Birth is stress, aging is stress, death is stress; sorrow,
lamentation, pain, distress, & despair are stress; association with
the unbeloved is stress; separation from the loved is stress; not
getting what is wanted is stress. In short, the five
clinging-aggregates are stress.
OP: However, I am unable to make out how ‘Suffering’ forms the
supporting condition for ’Faith’ to arise. Could this be clarified?
One learns of the Dhamma and grows to have faith in it, but only because he seeks an end to suffering. That's the connection of suffering to faith.
In the paper "The Spiral Path or Lokuttara Paṭicca-samuppāda" by Jayarava Attwood, he explains:
In particular, the Upanisā Sutta begins the sequence with faith
arising from suffering as a precondition. Suffering is the
culmination of the nidānas, and replaces jarā-maraṇa in the usual
nidāna sequence. This requires some exegesis, and some assumptions
must be made about how saddhā arises out of dukkha. ...
He seems to be saying that as a result of our experience of dukkha we
develop faith in the possibility of liberation. However, it is
not clear that saddhā does develop directly from the experience of
dukkha, or Buddhism would spontaneously break out everywhere. In
his 1966 and 1967 lectures, however, Sangharakshita filled in the
gaps a little: awareness of dukkha gives rise to “restlessness”,
which sets us “searching for something higher”, and once we contact
something higher then faith arises. Sangharakshita, in effect,
introduces three intermediate steps: restlessness, searching, and
contact with something higher.
OP: why is lokuttara paṭicca-samuppāda also called the ‘Spiral Path’ by > Bikśu Sangharakshita?
From the same paper, we see the suggestion that Sangharakshita called the lokuttara paticcasammupada the spiral path, to denote that it's a progressive path, as opposed to the lokiya paticcasammupada, which is the cyclic path, meaning repeating:
Dr Beni Barua took up the theme in his lecture Buddhism as
Personal Religion, published in the Mahabodhi Society Journal in
1944. It appears to be Barua who first used the terminology ‘cyclic’ and ‘progressive’ of the two forms of conditionality;
a terminology popularised by Sangharakshita in his writing.
Barua presents a progressive sequence of steps, but attempts
to locate this precise sequence in the Canon have not found it, and
it seems Barua may have used poetic licence with canonical lists. ....
Sangharakshita also highlights the singular nature of the Upanisā
Sutta (SN 12.23) in combining the two categories of
paṭicca-samuppāda (p.136). It was Sangharakshita who coined the
term ‘Spiral Path’ for this sequence, to contrast it with the
cyclic nidānas. 40
40 Sangharakshita has always taught the traditional
‘three lifetimes’ interpretation of the twelve nidānas, and often
makes use of the bhavacakka