1. For simple linear regression, the p-value of the coefficient is also the p-value of the model.
2. R square is the ratio of the variance of the DV that is explained by the model.
3. You may test the models on new data
What do you mean by "compare"? Are you talking about a one predictor vs a two predictor model on the same data? Or perhaps a transformed predictor vs a raw predictor? Or what?
You probably also need to know the sample size.