how is that the impedance is not dependent on trace length and only on trace widths ?
This question has previously been asked and answered several times. For example:
How can PCB trace have 50 ohm impedance regardless of length and signal frequency?
Should each trace carrying RF be 50Ohm in characteristic impedance? How?
How is xΩ impedance cable defined?
The key point is you should not confuse characteristic impedance (the ratio of voltage to current for a propagating signal on a trace) with the impedance of a circuit branch (the ratio of voltage to current flowing through that branch).
how can Altium suggest a trace width without me specifying the frequency ?
The characteristic impedance depends on the balance between inductance and capacitance per unit length of trace. Therefore it doesn't change (to a first order approximation) at different frequencies.
Is there a way I can calculate Impedance between any two given points on a trace for a given frequency ?
The characteristic impedance of a trace is not the same as the impedance between two points on the trace. It is the ratio of voltage to current that is required for a signal to propagate along the trace.
If the trace is long enough that the charcteristic impedance matters, then you can't actually define the "impedance between any two points on a trace" because there will be a delay between when a current signal is applied at one point and when a voltage is developed at the other point. Further the voltage won't depend only on the positions on the trace but also on what else is connected to the trace ends.
Instead you can define a scattering matrix (or S-matrix or S parameters) for the piece of trace. Or you can define Z, Y, or ABCD parameters, which are all equivalent.
If there is no such way in Altium(which I suspect), then how do people design Antennas these days ?
In any case, you do not want to use the Altium estimate for the trace width to achieve a given impedance to design an antenna. Altium will assume you want to confine the signal to your trace (and ground plane), rather than cause radiation. If you are designing an antenna you want a radiated signal, not a confined signal.
You can use a tool like HFSS to design an antenna.
Or you can use various more ad hoc methods that are known to RF engineers (for example, you could simply design an antenna that you know is too long for your desired frequency, and trim it back until it resonates at the desired frequency)