Actually, I don't agree with any of the statements......
In regression, the t-stat, coupled with its p-value, indicates the statistical significance of the relationship between the independent and dependent variable. The p-value is not an indicator of the generalizability of the model (i.e., will it accurately predict "outside" of the model?), but the probability of getting the result if in fact the null hypothesis is true (i.e., "no significant relationship").
The generalizability of the model will be determined by how well you designed the study and the scientific merit of the theories and hypotheses, not by any of the statistical output.
Considering only the significant relationships between independent variables and the dependent variables, the ones with the highest amount of influence will generally be the ones that have the highest beta coefficients:
y = x0 + B1x1 + B2x2 + ... + Bnxn + e