Since when are we able to discover interstellar objects similar to 1I/ʻOumuamua? Since when are our observation capabilities good enough to discover objects similar to the first discovered interstellar object 1I/ʻOumuamua (October 2017) with high probability?

Could we make rough estimate how frequent are passes of similar objects through the inner Solar System?

What could be the probability that during this century we will be able to gain more observational knowledge about interstellar objects?
In general terms we have had the observational capability to discover interstellar objects like this for quite some time - before digital imaging, photographic plates were used, which allowed accurate and verifiable measurements to be made. The issue is not so much in the observational and recording capability, but in collecting sufficient data to be able to compute an orbit. 

With a few hours of observation you can compute a path that allows further study on subsequent days. This usually assumes a circular orbit as a first approximation, but with increasing elapsed time after the observations the computed path increasingly diverges from the actual orbit. 

With observations over a span of days you can compute a better orbit, but again with increasing elapsed time after the observations the computed path increasingly diverges from the actual orbit.

With observations over a span of weeks you can compute an orbit that allows you to find the object again in subsequent years... and so on. Increasing elapsed time correlates to increasing divergence from computed orbits. 

So, with a moderate span of observations, we would find that an interstellar object is diverging from its predicted path (orbit around the Sun) and that it is passing through the Solar System instead of being part of it.

But with the greater number of automated surveys (especially compared to pre-digital imaging) that routinely flag asteroid and comet detections, the likelihood of interstellar objects being detected is greater now than in the past.

But someone has to be looking for it. The Minor Planet Center likely has a large number of objects in its database which are actually interstellar objects. But it's set up to correlate detections based on Solar System orbits and the interstellar objects will exist as unconnected short-path observations that don't fit to an orbit. Maybe someone could find more by mining the data, but unless they are still near enough to follow up with further observations these will be unverifiable. But it would be an interesting project!