We need the following figures:

M_{solar} = 1.98892*10^(30)kg

R_{solar} = 6.96*10^(8) meters

The mass of the black hole is M = 15 M_{solar}, so the parameter m in the Schwarzschild metric is:

m = M G/c^2 = 22.15*10^(3) meters

The r coordinate of point 1 is :

r1 = 300 m = 6.645*10^(6) meters

The r coordinate of point 2 is 10*R_{solar}:

r2 = 6.96*10^(9) meters.

It is important to realize that r1 and r2 are not physical distances, but just labels to indicate points in space. Distances and time intervals must be derived from the Schwarzschild metric:

ds^2 = c^2(1-2m/r)dt^2 - (1-2m/r)^(-1)dr^2 - r^2 d theta^2 - r^2sin^2(theta)d phi^2

Let's use this to calculate the distance from r1 to r2. You again use the fact that ds^2 is an invariant. At any point you can define local coordinates in which the metric is locally like
c^2 d T^2 - d L^2. Then dT is a time interval measured by the observer and dL a distance measured by that observer. Since the value of ds^2 for two given points is the same in al coordinate systems, you can extract the square of a distance between two points from the spatial part of the metric. Time intervals follow from the temporal part of the metric.

So, the distance dL between a point at r and r + dr lying along a radial line follows from:

dL^2 = (1-2m/r)^(-1)dr^2 -->

dL = dr/sqrt[1-2m/r]

If you integrate this from r1 to r2 you get the distance:

L = L(r2) - L(r1)

where I've defined the function L(r) as:

L(r) = sqrt[r^2 - 2mr] + 2m Log[sqrt(r) + sqrt(r-2m)]

I find: L = 6.9532*10^(9) meters.

To calculate the time interval at r1 which corresponds to 1000 seconds at r2, we can proceed as follows. Suppose at some coordinate time t a clock at r2 starts ticking and it stops when a proper time of 1000 seconds has passed. Both events are communicated at the position r1 using, say, a light signal. When the first signal is received a clock at r1 starts and when the second signal is received that clock stops and we record the proper time between the two events.

The coordinate time at which the clock at r1 starts is t + U where U is the coordinate time needed for the signal to reach the clock at r1, and it stops at time t + delta t + U, where t + delta t is the coordinate time at which the clock at r2 stops. So, the fact that U is nonzero doesn't matter here; both signals are received with the same time delay U. The coordinate time interval between the two events is delta t, which is the same as the coordinate time interval between the starting and stopping of the clock at r2.

We want to know what the clock at r1 will record. At a radial coordinate r the relation between a proper time interval dT (which is measured by clocks) and a coordinate time interval dt is:

c^2dT^2 = c^2(1-2m/r)dt^2 --->

dT = sqrt[1-2m/r]dt

So, the coordinate time interval corresponding to a proper time interval dT at r2 is:

dt = dT/sqrt[1-2m/r2]

This is, of course, also valid for finite time intervals:

delta t = delta T/sqrt[1-2m/r2]

The coordinate time interval between the two signals at position r1 is delta t, so the proper time interval that the clock there will register is:

(delta T)_1 = (delta t) * sqrt[1-2m/r1] =

(delta T) sqrt[1-2m/r1]/sqrt[1-2m/r2]

I find that 1000 seconds at r2 corresponds to 996.66 seconds at r1.

In case of a flat space time the proper times would, of course be the same. For the distances, it doesn't make sense to say that that would change, because the coordinates themselves don't have physical meaning in general relativity. They are just labels. You could say that if you introduce spherical coordinates in a flat space time and want to put the two points at the same distance as calculated above then the difference in the radial coordinate would have to be L and not r2 - r1.