Are these the net radiation at surface, and the complete energy balance at surface?
Yes, these are the correct terms.  The first equation is generally termed the 'surface radiation budget' and the second the 'surface energy budget'.

As @Deditos pointed out, additional terms for biological storage and flux can be added and are in fact important sources when considering a microclimate, and these would generally be placed into the surface energy budget.

Another form of the first equation is

Rn = ϵLW↓ − σϵT_s^4 + (1−α)SW↓

Where ϵ is the longwave emissivity of the surface, σ is the Stephan-Boltzman constant, T_s is the surface temperature, and α is the albedo (see Huber et al., section 3.2).

In certain circumstances, it is useful to set them equal to each other by solving for Rn, so you may also see

ϵLW↓ − σϵT_s^4 + (1−α)SW↓ = G + H + LE + (S + B)

Where B is the biological flux.