to the first question:
It is not very easy to say what your p-value exactly means, because it is general very hard to say what p-values exactly are. If you are testing in the intention of Neyman- Pearson you could say that your result is under the threshold of 0.05 and thus significant. But as you wrote that you have done more NHST Tests you have to correct your p-values for Family-wise error rates, because your Type 1 error increases every time you do a test using the alpha Niveau of 5%. Even though it may be significant a low p-value doesn't say something about external validity or how big your effect is. So it would be nice to look for effect sizes, in this case the Multiple R-squared that is printed in the
summary output in R. Maybe the official ASA statement for p-values gives you a clue how to interpret them: ASA statement.
It would be nice if you could describe your hypotheses more precise and how many tests you used.
To answer this question it would be nice if you could give an example of data that you use. I created an example with the airquality data set that is a base R data set. So you could reproduce my code.
fit <- lm(Ozone~ Wind,data=airquality) #setting up a linear regression model
plot(Ozone~Wind,airquality) # plotting the correlation
summary(fit) # get an overview about the model
abline(fit) # plotting the regression line
Given your question I thought that you wanted to visualise the regression line that would predict values from your model. I don't know what the
reset function does, I can't find it in the base packages. The
predict function would predict values of your output variable using your model. May you want to see what your model thinks the Ozone would be if the Wind has an value of e.g. 5. For more info you could look here.
I hope I could help you