Re-dyeing cotton, or cotton-rich, clothing to the same colour shouldn't be a problem. Dylan's wash'n'dye or whatever they're calling it now is quite good - use it in a washing machine. If it were me doing it, I would wash the clothing well first, then put two packs of dye covered by 500g of salt into the drum of the machine and plonk the damp clothing on top, then run it at 60° (the instructions say 40° but I think hotter is better). When the cycle finished I would then re-wash the clothes at 90°, to clear as much loose dye from them as possible, and then run the machine on empty with a high fill programme and a squirt of bleach to get loose dye out of that too. My next wash with the machine would be all darks too, just in case.
The quality of the dying seems much higher than the commercial dyes the clothes arrive with; you should find they hold their colour for years. These sort of dyes require a chemical reaction with the salt to lodge them into the fibres and are too expensive for most clothing manufacturers to use.
Changing colour is much more problematic because just about all clothing is sewn with synthetic thread which is almost impossible to dye at home. If you were desperate though, it might be possible to use a colour matched permanent marker to go over the seams and top-stitching, though I don't think it would last more than a few washes without needing to be retouched. Obviously you can only do this if the original garment is paler than the desired colour.
If however you want to change dark navy blue to black, just go ahead - the stitching is very unlikely to show. I've done it many times.