There are layers of “condensed” grammar and “hedging” to not state pure facts here. It could be translated roughly as

Sources/people are saying that Mr. L. W.’s group considers that the buy conditions are fulfilled and is preparing to pay Mr. Wright half the agreed sum (250K francs). The other half is to be paid once the aviator will be done teaching the three students he has committed to train.

1. On is used in its impersonal meaning. Without a broader context, I’m used Sources. (It’s really short for on nous assure)
2. The conditional here provides extra hedging on top of the on. I seem to recall (but may be wrong) that would is not available in this context in English. Present indicative would also be grammatical, but conditional is more usual.

Using conditional or present for the verbs “disposer” are both correct grammatically but it changes the meaning of the phrases.

Here the use of conditional implies a future action : ” we insure that the financial group (regarding fulfilled purchase conditions) will proceed to the payment of the promised sum of money”.
It means the purchase conditions have to fulfilled before they pay.
You could see this kind of phrases on official contracts for examples.
If you use the present : “On assure que le groupe financier (considérant les conditions d’achat comme remplies) se disposent à verser la somme promise.”/”we insure that the financial group (regarding fulfilled purchase conditions) proceed/are proceeding to the payment of the promised sum of money”.
You could see it means here that the purchase conditions have already been fulfilled and they pay.
Hoping it helps