Yes, one of the four dimensions in our "four dimensional space time continuum" is time but whether it is "the fourth dimension" depends on where you start counting!
Yes, "0 dimensions" would be a dot, but "1 dimension" is not necessarily a line. It could be any curve. For example, the set {(x,y)| y= x^2} is one-dimensional. Similarly, a plane is an example of a two dimensional set but a two dimensional set can be any surface.
A sphere is in 3 dimensions but it is not "3 dimensions" in the same sense that a point, line, and plane "are" 0, 1, and 2 dimensions- it does not encompass all of 3 dimensional space. And, in keeping with the previous examples, you should have "3D = all of space".
And "4D = time" is completely different from the others. "Time" does not have 4 dimensions in the same sense that the others have 1, 2, or 2 dimensions. "4D= time-space" would be better.
The number of dimensions something has expresses how many numbers you need to designate a single "point" in that thing. A "point" has 0 dimensions because you only have the one point to begin with so you don't need to "designate" it at all. To designate a point on a line (or curve) I could arbitrarily assign "0" to one point and measure from that to the point I want to designate and assign it the distance (positive in one direction and negative in the other). To designate a point on a plane, i could set up a coordinate system and use the two number, x and y. To designate a point in space, I need three numbers.
Physicists work with "events"- thing that happen at a specific point, at a specific time. We need three numbers to designate the point and one number to designate the time. That is what we mean when we say that space-time is "four dimensional" and that time is the "fourth dimension".
