How do I find parallel lines to the regression line with the standard error estimate? Is there any particular formula i could use to determine the line?

To get a line parallel to the regression line, you need to change the intercept (and not change the slope(s)). So, if your regression line is $y = bx + a,$ and $e$ is your standard error, then the lines would be $y_{upper} = bx + a+e$ and $y_{lower} = bx+a-e.$

To get the percentage of data points between the two lines, plug each $x$ from the data into $y_{upper} = bx + a+e$ and $y_{lower} = bx+a-e$ and then check if the corresponding $y$ from the data falls between $y_{lower}$ and $y_{upper}$