Yes, base on the moon is useful.
Main commercial reason to have the moon base is the difference in cost lifting the matter from earth compared the same from the moon.
It is not only 12 times cheaper energy-wise if you use non-rocket launch systems but the complexity and costs(energy and labor) involved in building such non-rocket launch systems (mass drivers or anything you may wish) on the moon compared to any other body in solar system.
No, the base it not obsolete after the interplanetary infrastructure is established.
Moon is a big possible source of main construction materials which we use today
- Iron, Aluminium, and others. The may lose their significance, but still, they are possible building materials, which can be used
The most importantly it's close to the Earth. Proximity to earth means fewer delta-v requirements for delivering the materials for any construction you would like to build near Earth or in Sun-Earth L1, L2 points, especially with mass drivers. And as long as there more people on Earth than in other places in space, demand for those constructions here will be more than in any other place, especially because building those constructions can be useful for Earth climate maintenance, energy supplies etc.
Generally speaking there no a lot of possible alternatives for the moon. Asteroids - water(hydrogen), nitrogen, carbon, construction materials. Venus - carbon. Jupiter and its moons - hydrogen, carbon, nitrogen construction materials. Mars - construction materials(con - atmosphere and genetically modified Martians dreaming about terraforming). Mercury - construction materials(small con - high delta-v requirements). So even with infrastructures on all those bodies, the significance of moon will be reduced, but not vanish.
after the birth of orbital space station and lunar base become obsolete, how could I repurpose this lunar base?This question is still salvageable if you put constraints and make the question more clear. $\endgroup$