There are a few imprecise propositions on evolution in your questions that make them hard to answer so they need to be rephrased.
how do we get to know that a gene is getting evolved from mouse to primates and then to human?
These are all extant taxa. Genes do not evolve from mouse to primates or humans, gene sequences evolve from a common ancestor, in this case your gene evolved from the gene in the last common ancestor of mouse and primates. The ancestral state of the gene sequence is not observable, because the mammalian ancestor is extinct, but can be estimated using Ancestral Sequence Reconstruction (ASR) using many mammalian sequences as input. Phylogenetic trees can be constructed to get an impression of how sequences diverged from each other.
How do we find out that the gene is under selective pressure?
Traits are under selective pressure, pressure is a general driving force of evolution by natural selection. Traits contribute to the overall fitness of the organism. Changes in traits (e.g. by mutations) contribute to changes in fitness, either positively, negatively or neutrally. Detrimental changes, e.g. mutations that cause loss of function in essential genes, are negatively selected, or under strong purifying selection. This can be concluded from sequence conservation. Genes that are highly conserved among many species can be under purifying selection.
A common indicator of direction and magnitude of selective pressure is the Ka/Ks ratio.
Why is that particular gene is getting evolved ?
"Why" is difficult to answer. There are several driving forces in genetics that are the same for all genes but don't affect all genes equally:
- Mutation rates
- Gene loss/gain
- recombination
- Gene/whole genome duplication
- environment and life style/ and changes thereof, e.g. changing habitat
- effective population size/ bottlenecks
Is there any bioinformatics tool through which we could answer all these questions which I have mentioned above?
All Phylogenomics tools in general address some of these questions. Most relevant are tools to build phylogenetic trees. While reading on phylogeny you can start with MEGA6 or 7.
You probably wanna read the stuff Motoo Kimura wrote.
August 2016 issue of The Scientist magazine has some interesting articles on this topic.