I have an dataset of fasta sequences. This proteins are not complete (My sequences have 700 nucleotides,while complete sequences have 1725 nucleotides)I would like to know if i can make an population genetic analysis from it(like TAJIMA-D test) and similars.
It very much depends upon what type of analysis you want to perform. For a Tajima's D, all you would need is a single nucleotide sequences in a sample of individuals, so yes you can. Whether or not the sequence came from a gene or any other sequence is not relevant to whether you can compute Tajima's D (although the type of sequence will likely affect the resulting D).