(...)
This reminds me of something I've been meaning to document for a while (I'll try to get to it soon). After estimation of a single-equation model the new accessor $model retrieves a bundle containing all the regular model accessors plus some other information. To get the regular accessors you just use the accessor-name, minus the $-sign, as the key, as in

ols y 0 x
bundle b = $model
series uhat = b.uhat
(...)
Anyway, the two things you mentioned weren't included in the $model bundle for a fixed-effects model, but now they are (in git and snapshots). Ss, for example, the script

<hansl>
open abdata.gdt
panel WAGE 0 EMP CAP
bundle b = $model
print b
</hansl>

produces:

bundle b:
 fixed_effects_F (bundle)
 xlist (matrix: 1 x 3)
 lnl = -2200.21
 ahat (series: length 1260)
 command = panel
 hqc = 4950.54
 Fstat = 41.776
 n_included_units = 140
 yhat (series: length 1260)
 DW = 0.928223
 ylist = 4
 T = 1031
 depvar = WAGE
 within_F (bundle)
 bic = 5385.66
 sigma = 2.20166
 Tmax = 9
 sample (series: length 1260)
 uhat (series: length 1260)
 vcv (matrix: 3 x 3)
 trsq = 895.803
 aic = 4684.42
 coeff (matrix: 3 x 1)
 df = 889
 Tmin = 7
 within_R2 = 0.0213909
 ess = 4309.24
 ncoeff = 3
 rsq = 0.868868
 rho = 0.367727
 stderr (matrix: 3 x 1)

Note the keys "within_R2" and "DW".