Question

can a single gene can influence multiple traits

Answer 1

Yes.
A protein produced by multiple genes are cased by fusion genes.
Usually a protein is translated from a mRNA which is transcribed from a DNA. After transcription, RNA is rearranged by so-called RNA splicing in which some of short sequences are selected(Exon) or deleted(Intron). During the splicing two different genes can join together and it is called trans-splicing.
After trans-splicing, mRNA is translated into a protein, so the protein has two genes. Most cases these fusion genes are oncogenes which cause Cancerous diseases.