Can we create custom gene/protein?
Yes, there are well established methods for synthesizing DNA with any sequence you want. Several commercial companies will accept DNA sequence (a text file) and generate the DNA for you. Genscript for example is well known.

Synthesizing the protein can be bit more tricky, depending on what it looks like and what you want it for --- proteins are way more heterogenous than DNA. There are commercially available cell-free protein synthesis systems that might be useful if you are merely interested in a peptide. Most people express the protein of interest in cultured cells though. In either case there is some biochemistry work to purify the produced protein. Genscript provides protein synthesis services as well. (No, I'm not paid by them, just don't have the energy to google other companies :)

In most cases, this works fine, and with a bit of tweaking you can produce quite large amounts. But for some proteins that depend on posttranslational modification for their function, expression can be difficult: see Can any enzyme be produced?