Learn English – take place in + time

When an event takes place it simply means that it happened or occurred. I consider this to be idiomatic because this has nothing to do with the definition of either take or place. I can't find a source that agrees, so I'd say that, at the very least, it's a phrase with only one possible meaning that's frozen in time so to speak. In other words, these words only have one application, which is unrelated to their traditional definitions.

With takes the place [of], place means stead, as in instead. It's another way of saying substitutes for, replaces, assumes the role of, or takes the role of. It's literal, with place meaning position rather than a location.

It means the seminar will take place seven days after the next Tuesday. Assuming it was said today, it would mean Tuesday 22nd September.

I can't explain the grammar behind it because it's a standard phrase (in British English, anyway). You'll find the definition in the Oxford Dictionary under Phrases.

a week on ——
Seven days after the specified day or date:
‘we’ll be back a week on Friday’