Hello everyone!

I have a panel data for labor productivity for 74 countries for period of 1992-2016.I am trying to understand the convergence rate based on romers model of convergence.
I attach also the data

I am using xtregar for my model and getting such results.

Code:
. xtregar ln_diff ln_prod_lagged t18-t19 L1.ln_diff L2.ln_diff, fe rhotype(tscorr) twostep

FE (within) regression with AR(1) disturbances  Number of obs     =      1,628
Group variable: id                              Number of groups  =         74

R-sq:                                           Obs per group:
     within  = 0.0917                                         min =         22
     between = 0.0056                                         avg =       22.0
     overall = 0.0043                                         max =         22

                                                F(5,1549)         =      31.26
corr(u_i, Xb)  = -0.9112                        Prob > F          =     0.0000

--------------------------------------------------------------------------------
       ln_diff |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
ln_prod_lagged |  -.0742815   .0073197   -10.15   0.000     -.088639   -.0599239
           t18 |   -.038016   .0108618    -3.50   0.000    -.0593213   -.0167108
           t19 |   .0602955   .0109165     5.52   0.000     .0388827    .0817082
               |
       ln_diff |
           L1. |   .0431449   .0222561     1.94   0.053    -.0005104    .0868002
           L2. |  -.0367265   .0210011    -1.75   0.081    -.0779201    .0044671
               |
         _cons |   .7583084   .0742463    10.21   0.000     .6126746    .9039422
---------------+----------------------------------------------------------------
        rho_ar | -.03962128
       sigma_u |  .09476397
       sigma_e |  .09042197
       rho_fov |  .52343382   (fraction of variance because of u_i)
--------------------------------------------------------------------------------
F test that all u_i=0: F(73,1549) = 3.58                     Prob > F = 0.0000
I have several questions regarding the results I am getting, and will be grateful if someone could answer.
1. I am getting 0.52 for rho_fov and with no any linear model i cannot increase it, does it mean this models are not good to use in case of my data?

2. My second question might sound weird but is it possible after estimation of coefficients somehow go deeper and inderstand what the coefficient/rate would be for specific country, for example Armenia as each country has different moving path and the speed can be different.

3.Are GMM models more appropriate for such analysis? I do not understand very well dynamic panel models and what is going on in background, so for now trying to stay away from them.

Thank you very much in advace!
Best,
Sara Zakaryan