You can. Some factors to consider are codon bias in your target organism as translation efficiency is strongly tied to tRNA availability. This means that using the same codon too close together can deplete the pool of amino acid bound tRNAs for that codon so it is good to use a variety where possible in the ratios of the codon bias for the organism. Also check your resulting nucleotide sequence for secondary structure as hairpins can impact on transcription efficiency and the resulting transcripts can cause RNAi reducing expression.

Bioedit, UGENE or CLC can do that for you, but it may not be entirely accurate

If it's an organism that has had at least some of its genome sequenced, try using BLAST. a "tBLASTn" search will compare the protein sequence to translated nucleotides.

Good luck!

Yes you can predict a DNA sequence that codes for a protein. However, due to most amino acids having more than one codon the possible DNA sequences are vast. If what you really want is to determine which code the organism uses for that protein, your best approach is likely to compare sequence information. If your organism does not have a genome sequence (or does not have good enough data for your favorite protein and its possible gene) then look to related organisms. There will be codon usage differences and sequence variation but it could be enough to work with.

Another caveat is that you can predict a plausible sequence for the exon, but not introns, promotors, and other parts of the gene.

You could get predictions based on the structure of homologous genes in closely-related organisms. But you'd have to follow up on any predictions with bench work.

What's your overall goal? Do you want to clone & express the protein? Knowing more about what you want means we can give better advice.