Avoiding spurious regression in meta-regression using stationary variables like GDP

I have been reading everything I can get my hands on about spurious regression but can't seem to definitively find out what is best in regressing cross-sectional data including non-stationary variables.

Example data:

Country    GDPyearofstudy         Popdensyearofstudy   Year of study Total(2013$)

UK          2462484285580                 2.63                   2011       0.5
Brazil      2143067871760                 0.23                   2010       1.5
USA          13095400000000                0.34                   2005       2.3
USA          14958300000000                0.37                   2010       1.5
Total observations: 49

I am conducting a meta-regression of values obtained from studies between 1990-2011. My y variable is Total (2013$) and my x variables include GDP and Population density to help understand the valuation. The year the study was undertaken is also included. I was told using GDP and Population density could skew results through being non-stationary, so I attempted to calculate GDP growth as 100*log(GDP/lagGDP). As I only have one observation for some countries however, this has mostly produced errors as there is no lag on a single observation.

My questions therefore are:

1. Do I use GDP and Population Density for the year the original study was taken, or
2013 which I have standardised Total(2013$) to?

2. If this is cross-sectional, do I have to worry about GDP and Population Density
being non-stationary?

3. If they are non-stationary, will using the log of each be enough, or do I have to use GDP growth which in my case mostly fails to produce a result?

4. Can I simply adjust the standard errors?

I have run regressions using GDPyearofstudy; GDP2013; logGDPyearofstudy; logGDP2013; GDPgrowth and all fitted vs. residual plots look fine, Breusch-Pagan test is fine and all variables show a Pearson correlation of <0.6.