2
Like any curve construction, you would use the prices of traded assets to construct the curves. For example, in the standard LIBOR, people use FRA, futures, and swaps referencing LIBOR to construct the LIBOR curve ( say 3 months or 6 months). For SOFR, you can use SOFR futures and swaps, so don’t think there is much difference, the problem at the moment is ...
1
I believe the duration constraint and the proceeds constraint are not self consistent. You cannot satisfy both. The duration constraint alone fixes $N_1/N_2$ and $N_3/N_2$, so you cannot also satisfy the proceeds constraint.
1
The quoting convention for almost all bonds is clean (without accrued) rather than dirty (with accrued, all-in).
Generally, bonds are quoted dirty in two cases:
1 A distressed bond that's expected to default (after default it trades on recovery)
2 In some foreign markets, it's just a market convention that all bonds are quoted dirty. (For example Brazil ...
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