It is not necessary to use the direct article as part of the name of schools, museums and churches. Thus I suggest the names of all four places in Przedbórz are fine without the.
If you want to say you went to (attended or visited), you can also omit the definite article with the schools and the church. With Folk Museum it sounds more natural to me to say 'I went to the Folk Museum'. This is because "folk museum" can refer to a type of museum, a folk museum as opposed to a science museum.
As for universities in the USA, there is no rule. Some universities like to include the as part of their name. To some this is an attempt to sound "more special" because the definite article refers to a specific (i. e., one) university, as in
The Ohio State University
The University of Texas at Austin
and other universities that include the in their official name. But outside of strict rigid adherence to official designations/names, people usually refer to them without the definite article or even their initials: OSU or UT.
(I have no idea what the "official" name of John Hopkins University is, but if it includes the, then it just works as the above two examples. And I believe the main concern of your question is whether you have to or should include the as part of the English names of the four places in Przedbórz, and my answer to that, again, is no.)
The same thing applies to museums some of which have the as part of their names and others of which do not. I suppose it's the same for churches, but I think the number of church buildings/congregations that use the as part of the name are few.