That's a tough concept map in the uploaded image. Without some kind of "word bank," the problem is made tougher because several answers could work for each concept map bubble.
A gene is a specific part of a chromosome. That means it is a specific sequence of DNA base pairs. The gene is identified by that sequence. mRNA doesn't identify the gene. mRNA simply copies down the gene sequence and takes it out of the nucleus to a ribosome. Then the mRNA is translated into a chain of amino acids which then becomes a protein.
I would say genes "are used to produce" (far right bubble) specific proteins as my previous paragraph explains. That is also what you stated in your question, so no changes there.
The last bubble is tough. "May be used for ...." I'd go with "protein synthesis." Protein synthesis has two steps: transcription and translation. Transcription is the mRNA copying down the gene from the DNA. Translation is the ribosome and tRNA using the mRNA to make the amino acid chain (protein). Without the gene, protein synthesis would be made much more difficult.