This might be because the death certificate says that "die Vorsteherin des Krankenhauses angezeigt [hat]", which means that she died in a hospital. The address given on that certificate is Altstraße 42, which is actually a parallel street of the Trierer Straße.
About the question if the first letter in the first certificate is really a T: I think it is. I double checked with my file of Süttlerlin-letters, and the r-letter is started in the "middle height" when you write it. This fits with where the second letter of the word is started. The second letter is imo a bit "overwritten" over the first one, which makes the first letter look like a F.