The other question has some very good detailed answers, worth reading, but briefly and more specific to your question:
Would there not be interactions between their Oort cloud objects and
the planets of the Solar system? For example, the outer edge of the
Sun's Oort cloud is approximately 100,000 AU away. So, if another star
comes at a distance of 1 light year from the Sun, its Oort cloud
should similarly go through the inner solar system.
While very little is actually known, it's not crazy to think that smaller stars might have smaller oort clouds and larger stars, larger ones, though there's a great deal of uncertainty on what an average oort cloud is, how far an average one extends, and how densely packed they are.
First part first, how often does a star pass within one light year of our sun?
Not very often. Ballpark, maybe every million to couple million years or so. The last time was 70,000 years ago, a small star, 15% the mass of the sun. See here.
In the fly-by section of that same wiki-article, it says a star passes that close (0.82 light years or less) about once every 9 million years.
Scholz's star is quite small, only about 15% the mass of our sun, and it's unclear if it had an Oort cloud that extended .82 light years at all, so while it passed through our Sun's Oort cloud, it's unclear if the inner solar-system passed through it's Oort cloud, assuming it has one. It's also possible that the sun stole much of Scholz's star's oort cloud during the fly-by, but that's just speculation.
Did Scholz's star send Oort cloud objects heading towards Earth? That's a good question and the answer is, probably, but we don't know, because if it did, it would take longer than 70,000 years for any re-directed Oort cloud comets to reach the inner solar-system. By the same article, an estimated 2 million years for re-directed Oort cloud objects to reach the inner solar system, so, in about 1.93 million years (give or take), we'll start to see what Scholz's sent our way. :-)
In 1.36 million years, Gliese 710 could pass within 1 light year of Earth. The estimate is 1.1 light years plus/minus .577 light years. Gliese 710 is larger than Scholz's, about 60% the mass of the sun but we know nothing about how large or how dense it's Oort cloud might be. But, very generally, it seems likely that the Sun has passed through another stars Oort cloud at some point, perhaps every 1-10 million years, perhaps every hundred million years or so, but it seems reasonable to me that has happened and will continue to happen, on rare occasion.
2nd question, what would happen if the inner planets passed through another star's Oort cloud.
If we use our Oort cloud as a model, and, warning, these estimates are enormously ballpark, but, a trillion Oort cloud objects 1 KM or larger and the Oort cloud extends between 100,000 and 200,000 AU (lets say 150,000 as a middle estimate), that works out to one 1 KM or larger object per cubic region of space about 15 AU across. That's 3/4ths the distance between the Sun and Neptune, so if you figure just one, 1 KM or larger comet or object in a 3D space over such a vast distance, most would pass by the inner planets unaffected. The occasional one would get it's orbit measurably altered with a fly-by of one of the gas giant planets and rarely, there would be an impact. Now presumably there's more smaller stuff in Oort clouds too, so there should be smaller impacts more frequently, though there's almost nothing that's actually known about how dense Oort clouds are, so anything beyond "infrequent", is impossible to say.
Passing through another Stars Oort cloud should take tens of thousands, perhaps 100,000 years years or so, so there probably would be the occasional impact on a planet here and there, but on a human time scale, significant impacts should be very rare.