Emitter-collector resistance
To understand this you need to look at this sort of graph for a BJT: -

Picture from here.
So, choose the line that most corresponds with the base current you are using and see how how much collector current you might have for a given applied collector-emitter voltage.

(if we) have a constant base current , which is producing a constant (almost)
current, now is this correct to say the emitter-collector resistance
is almost zero, since it's passing current?

We would say that the collector-emitter resistance is high when the BJT is biased in the way you describe. This is because even though the collector-emitter voltage may be increased, there is still pretty much the same collector current.
We refer to this as the dynamic impedance of the BJT in that \$\dfrac{\Delta V_{CE}}{\Delta I_C}\$ is quite high.

but there is no collector supply voltage

Yes there is; the continuity tester may be producing a volt or so.