From a geneid you can get the information as XML from the NCBI with EFetch. e.g. for GeneId=2.

http://eutils.ncbi.nlm.nih.gov/entrez/eutils/efetch.fcgi?db=gene&id=2&retmode=xml

and you can then get the accession of each RNA sequence under: (...)/Gene-commentary_products/Gene-commentary/Gene-commentary_type[@value='mRNA']/Gene-commentary_accession (use XSLT/XPATH to extract this information)

and for each accession you get the DNA sequence with EFetch.

http://eutils.ncbi.nlm.nih.gov/entrez/eutils/efetch.fcgi?db=nucleotide&id=NM_000014&rettype=fasta&retmode=xml

Yes there is if your organism is in Ensembl - BioMart. Here is how you'd use the web interface, assuming that you want human sequences:

1. Go to BioMart and click MARTVIEW
2. Select database = Ensembl Genes 57
3. Select dataset = Homo sapiens genes
4. Click "Filters" to the left and open the "Gene" selection
5. From the dropdown box, select the IDs that you want to use (e.g. UniProt/TrEMBL)
6. Either paste your list in the box or upload the file
7. Click "Attributes" to the left, select the "Sequences" radio button and open the "Sequences" tab
8. Select what type of sequence (e.g. unspliced transcript)
9. Click "Results" (in menu bar, top-left of page)

This will return the first 10 sequences. You can download the rest as a file. There is also programmatic access to Ensembl: Perl API, biomaRt for R Bioconductor.

If this doesn't work for you, the Bioperl library should be able to retrieve sequences given IDs.

Thanks for your answers! I could not try with BioMart as my organism is not present on Ensembl. I forgot to precise that I am working on Chlamydiales.