I use Rate4Site, and it works fine for me.

I think it is important to spend time to calculate dN/dS. A profile gives you very few information compared to a dN/dS analysis. It is largely admitted that the dN/dS analysis is reliable and informative. Many publications use this method.

Codeml uses lot of computational resources. You can use MapNH instead, that is really light and faster. It does a good approximation. The results are substantially the same.

A sequence logo (assuming you're referring to Tom Schneider's work), and dN/dS ratio are measuring two very different features. The sequence logo is telling you the conservation of single residues, while the dN/dS ratio is telling you the ratio about selection pressures at the codon level. The sequence logo (at the amino acid residue level) does not provide any information about non-synonymous substitutions and therefore does not provide the total picture of a residue at a position.

For example I have a three amino acid peptide: ACF, I can have 16 different sequences that encode this, but a sequence logo at the amino acid level hides this information, all three residues would appear equally conserved, even if 2/3 residues are coded with the same codon while the third uses all of its codons. You miss the whole picture: the 2 residues with the same codon might be under purifying selection while the third may be under neutral/no selection.

I would do the codeml run, it is worth it if you are interested in exploring selection pressures acting on specific sites in related proteins. It will take a bit longer, but it is not a prohibitively large amount of time.