Trust a native speaker and linguist - I stand by my exegesis. Why make a text more complicated than it is? I live with and in this language for more than 62 years, with German and other folk songs about 50 years.
The subjunctive is necessary because of oratio obliqua = dependent speech. The use of the subjunctive is now widely forgotten in modern German everyday speech.

3. Bird: "I'm looking for my love everywhere and am afraid she couldn't be here. But if you are, console me birdie and enclose me in your white hands." That makes a lot of sense!
Note the difference: "tröst mich Waldvögelein" (apposition to me): console me, the birdie and "tröst mich, Waldvögelein" (direct address): console me, oh birdie!

Wolfgang - schließen/Schleuse same stem. Having seen a sluice working it is obvious. Old form of schließen in our hymnal: "heut schleußt er wieder auf die Tür ..."