The model I have run is a simple multiple linear regression. The model looks like a great fit, but R is telling me otherwise. My question is 3 fold. 1) How do we estimate linearity (not visually) 2) How do we solve to make the model linear. 3) What are the R packages that help with these tasks. Below I use the R packages "gvlma" to test for linearity "Global Stat".
None of these are necessarily a problem at all, depending on what you want to achieve.
If you want a "best linear approximation", there's one sense in which you already have it (and the fit you have will be quite close to some other senses as well).
If the linear fit is suitable for whatever your purpose is, having mild lack of fit or mild heteroskedasticity is not necessarily of much consequence at all (ignore the p-values, those aren't telling you anything useful abut whether your linear approximation is good enough for some purpose; if you sample size is large there will almost always be low values).
Since you haven't made it clear what your linear model is being used for, it's very hard to give advice about how to deal with it (or whether there's even a need to).