Science is not about assuming, it is about proving. So no, it is not safe to assume such a thing. If there were no phenotypic differences then all animals would be the same. To be different, there have to be both phenotypic and genetic differences. So no, your statement is a tautology which says 'if we assume evolution is true' then mutations are the cause of phenotypic differences. There is no proof of that.
. An example of this are a group of genes found in virtually all multicellular organisms called the Hox cluster. This locus is a major determinant of the overall body plan of the animal. It looks like it went through several duplication events throughout evolutionary history. This is still an area of active research, but where it has been tested, the mutations to the Hox cluster have been experimentally verified to be responsible for the visible changes of the organism (i.e. more legs, wings etc).
That is not correct. It is again saying that if evolution is true, those changes are due to mutations. You and evolutionists seem to forget a very simple thing, the phenotype of the organism has a purpose and has to be in accordance with other parts of the phenotype (what we see - arms, legs, etc). It is not there due to luck. The problem with the Hox genes and evolution is that they are not what is important when it comes to development. It is the program controlling development that matters because everything has to be done in proper order. Each time you make a cell for example you have to make sure it is able to get nutrition, oxygen, be able to excrete wastes, etc. So changes to the phenotype cannot be made stochastically (at random) they have to be properly programmed to be in accordance with all the rest that is going on in the organism's development.
I am unaware of anything in science that has been formally proven.
It is the program controlling development that matters because everything has to be done in proper order.
Yes, the Hox genes encode for factors which are "master switches" for all of the accessories associated with a specific body part (i.e. leg, wing)