Sure, that is one way of accomplishing your task so long as you do blending/interpolation to smooth the pixels in between. See these slides (esp. the last slide) or this survey for some literature on image warping and registration.
Thin-plate spline or "surface spline" problem
One reasonable approach would be establish point correspondences $r_1, \ldots, r_N$ and $w_1, \ldots, w_N$ as you have done already then solve the following problem:
Find the 2D transformation model $\mathbf{p}=\{c_1,...,c_N,A,t\}$ s.t.
$$w_i=f(r_i)=Ar_i+t+\sum_{k=1}^{N}c_k\phi(d_i),$$
where $\phi(d_i)$ are radially symmetric basis functions (RBF). An example RBF choice is $\phi(d_i) = d_i^2\ln[d_i^2]$, where $d_i$ is a distance of your choice, e.g. Euclidean $d_i=\|r_i-r_k\|_2$.
Under certain thin-plate spline conditions not detailed here, this problem can be cast as a linear system $\mathbf{L}\mathbf{p}=\mathbf{w}$:
$$\begin{bmatrix}\mathbf{K} & \mathbf{P}\\\mathbf{P}^T & \mathbf{0}\end{bmatrix}\begin{bmatrix}\mathbf{c}_{N\times2}\\\mathbf{A}_{3\times2}\end{bmatrix}=\begin{bmatrix}\mathbf{r}_{N\times2}\\\mathbf{0}_{3\times2}\end{bmatrix},$$
where $\mathbf{K}_{ij\,\,[N\times N]}=\phi\left(\left\|(r_i^x,r_j^y)-(r_j^x,r_j^y)\right\|_2\right)$ and $\mathbf{P}_{N\times3}=\begin{bmatrix}\mathbf{1}_{N\times1}\left|\mathbf{w}_{N\times2}\right.\end{bmatrix}$, and then solve for $\mathbf{p}$.
You can then apply the transformation model $\mathbf{p}$ to every pixel in the original/control image, and use 2D interpolation to get the final result.
And to answer your second question, assuming you are using OpenCV's CvPoint structure, you can just do the following:
cv::Point newPoint( oldPoint.x + xoffset, oldPoint.y + yoffset )
