Does the sentence "Jewish immigrants to our country has made many contributions" show proper subject/verb agreement

This sentence does not show proper subject/verb agreement. When it comes to this agreement, if the subject is in the plural form (like here, for example - Jewish immigrants to our country is in plural), then the verb also has to have a plural form. So, instead of has made, you need to use have made in order to show the proper agreement.

No, the correct format would be: Jewish immigrants in our country have made many contributions.