As your primary observations are counts, you should use an analysis method that is designed for counts and thus models observations with 0 counts directly. A Poisson generalized linear model with log link is a standard way to start.
As Kjetil B Halvorsen said in a comment, you use an offset, log(area), in your regression to account for the area corresponding to each observation. Then you can interpret your results of modeling counts in the units of individuals/1000 hectares that you desire. See this page among many others on this site.
It's possible that a simple Poisson model won't be adequate, in that the equality between variance and mean for a Poisson distribution won't adequately describe your results. A "quasi-Poisson" model, in which confidence intervals are based on other-than-Poisson variance, or a negative binomial model could be next steps in that situation.
It's not clear from your description that a mixed model ("MM" in your abbreviations) would be needed here. Whether you need to consider a "generalized additive" ("GA") model has to do with whether simple functional forms of your covariates are adequate in the linear predictor of log(counts). I'd start with simple linear modeling of covariates in a Poisson generalized linear model, as if that works it's usually easier to explain to others.
