I can't exactly answer 1 and 2, but on 3...
Yes for Shadow Hearts, as it is pretty much a direct "prequel" to Covenant, but as for Koudelka, if you are really desperate to learn about some of the stuff in Shadow Hearts (emigre document (skull book) and such, then yes. Heck, Koudelka even comes in during Shadow Hearts 1! And those Neam Ruins you visit in Covenant? Why, that's actually the old Mansion in Koudelka! See how it comes around full circle? Because it doesn't really fucking matter.
So yes for Shadow Hearts, big maybe on Koudelka, if you really want to see the big circle. Koudelka's battles are extremely different from Shadow Hearts, by the way.