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It is called an intercept.
A curve (or line) whose domain does not include the value x = 0.
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 location where the curve in question crosses the y-axis.
There is no specific word for a line that curves up because there are many different ways in which a line may curve upwards. There are polynomials whose leading coefficient is positive, a power curve with positive exponent and base greater than 1 or a curve which increases asymptotically towards a limit (for example y = a*[1-exp(-bx)] where a and b are positive constants and x > 0).