Yes, there are some programs for such an analysis but they are not free programs mostly. Alamut is one of the very well known programs.

There are some programs which are trying do give you an integrated metascore, I mean a score in which prediction of impact on protein structure and phylogenic conservation are integrated, such as CADD and VEST. But in practice, we use all the scores that predict an impact on protein structure (such as SIFT, Polyphen, LRT, Mutation Taster, Mutation Assessor, FATHMM... see the ANNOVAR site for further explanation) and categorize them mainly into 3 broad categories based on the results they give: disease causing (D), potentially disease causing (P) and tolerated (T). Then we estimate the probability of a disease causing mutation on the basis of how many software predict either D or P. It's not a precise estimation, and not a biological proof. It's only an argument which have sense if it converges with other arguments.

If you want to visualize a variant, no need of Alamut: UCSC genome browser do quite the same for no fees (you can annotate a locus with conservation scores such as PhyloP or GERP++, frequency annotation such as dbSNP142 or ExAC, and prediction of impact on protein structure too. To my knowledge, you can't have directly the conversion between g.DNA and c.DNA nomenclature, but you can visualize the codon numbers for a given transcript, which makes the translation not too difficult to obtain).

I would recommend trying dbNSFP. dbNSFP compiles prediction scores from 14 prediction algorithms and 6 conservation scores. Two of the prediction scores/tools - MetaSVM and MetaLR are based on the scores/predictions from about 18 prediction tools. dbNSFP could be used as plugin with Ensembl's variant effect predictor (vep).