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You always use some model (i.e. function) to fit experimental curve. If you do not know the kind of curve (linear, parabola, Gauss, etc.) you can try to fit with different functions and then compare the residual sum of squares and coefficient of determination of those fit functions. I use MagicPlot for curve fitting, you can try to find something in MagicPlot on-line help.
yes
Linear interpolation is used as a method used in mathematics of constructing a curve that has the best fit to a series of points of data using linear polynomials.
the formula
Draw a line/curve of best fit and read off the value from the line. The alternative, which requires more effort but is usually more accurate, is interpolation.