Hi Karen,
For our fitting models we use the package called Lmfit and the default optimiser is the Levenberg-Marquardt or leastsq .
The standard errors for the fitted variables are automatically calculated from the covariance matrix, (the square root of the diagnoal entries of the covariance matrix).
You can find out more about the optimiser and statistical results at Performing Fits and Analyzing Outputs — Non-Linear Least-Squares Minimization and Curve-Fitting for Python