Both of the cakes you’ve shown have been carved before being covered with fondant. It also looks like they’ve only used one large piece of fondant to cover the entire cake. If you’re not experienced at covering cakes with a large piece of fondant (“The Mat” is an awesome tool to help with this) I would recommend you covering each tier separately. If you cover the tiers separately I would recommend stacking the cakes without frosting and carve at the same time so that you get the look you want. The first time I carved I was scared to death but carving little bits of cake at a time made it easier. You can always mix discarded cake with icing to make unusual base shapes and then cover everything with fondant.
You will want to be sure to include a good internal support system. Anything over 4 tiers I use “single plate system” (SPS). You can find these on line or at your local cake supply store. Since you are going to be traveling a distance with the cake this might be a good option. Typically I am able to just use bubble straws under each cake round (at least 4 per tier) to give support. Just make sure they are all level.
They’ve also air brushed color to give dimension which takes your cake to the next level. If you don’t have an air brush machine you can achieve dimension using petal dust.
My figurines tend to be about 3" – 4" in height. You can use spaghetti as an alternative to the cocktail skewers for internal structure and a way to attach them to your cake. It is a great edible alternative. I attach heads, arms, legs, and feet with spaghetti all the time. You can make the figurines from gum paste or fondant with tylose powder. You will have a bit more “play time” with fondant as it doesn’t dry as quickly as gum paste. You could also make them out of modeling chocolate (a tasty alternative). It is a more pliable and forgiving but you have to cool frequently to set the chocolate. The warmth from your hands will cause it soften pretty quickly. No problem making your figurines well in advance. I do it all the time. Doing them in advance will help eliminate stress (I don’t work well under stress and I’ve been selling cakes for quite a while now) and give you time to remake if you’re not happy with the outcome. As mentioned earlier, store them covered and in an area that is dark. Many times I just moisten the bottom of the figurine with water and they stick pretty well. Royal icing and a piece of moistened fondant are also great choices. You could also use coffee stirrers or small straws as anchors in the cake to help secure them.
Best of luck!