Hi Wayward,
Welcome to the forum. I think you'll find a wealth of knowledge here to help you with your endevours. To answer your questions, leather quality will have a profound effect on your carving and dyeing. A lot of times a toolable (veg-tanned) leather will have hard spots. These spots did not get much of the tanning oils if any at all. This will affect the way the dye penetrates and shows. For now, I would stick with the cheap stuff until you get up to speed with actual projects. Then if you plan to do things for profit, I would upgrade to the best leather you can afford, and charge accordingly.
Spirit dye (alcohol based) dye (fiebing's) will dry out leather more-so than water based (eco-flow). However, water based dye takes a longer time to dry between coats. I am in agreement with Twin Oaks about speed drying vs. cool drying. The faster you dry the harder it will be. If you want to make leather more pliable, you can use Lexol conditioning solution to soften it up.
To actually see someone carve will probably help.
on carving leather. It's just a simple video with a person carving, but you'll get the idea of how it goes.The uneven dying could be a number of things. Are you using an antique stain, water based dye, alchohol based dye? All of these have a different method of application, so I'll need a little more info before I make any suggestions there.
By the way, welcome to the addiction.
Marlon