Whatever tree I get, once it has the shape, can it be changed?
The trees we use for bonsai keep growing so they are pretty much infinitely changeable. All you need is vision and time, plenty of time. Most of us think nothing of chopping a tree down to the first branch to get some taper and a bend in the trunk then growing it all again into a new tree. Sometimes restyle is less radical but still makes big changes to the overall appearance.
Sometimes, just changing the planting angle will make the tree seem like a completely new bonsai.
Even thick, old trunks and branches can be bent and twisted by hollowing them out to reduce stiffness of cutting some of the wood away to enable bending but that's pretty advanced horticulture.
We can also make less radical changes just by wiring and bending the branches into different shapes.
On the other hand, many trees have very stiff and brittle wood so it becomes increasingly difficult to make changes to the basic structure unless you use some advanced techniques or chop a lot off and regrow.
Another question is this. Let’s say I get a trunk cut to start. I don’t know how it would grow, do I let it just grow and then shape it?
This is something that probably needs experience or faith. Some species grow back easily after a cut and some don't. Some grow quicker and some slower. Some are easily shaped and some are not so, unfortunately, different approaches for different groups of trees but, in general, I suspect that chop, let it grow, shape or chop again, let it grow and repeat is the formula for many bonsai now.
Many of the conifers , junipers in particular, are the closest thing we can get to 'instant' bonsai' provided you choose your starting material wisely.
I'd encourage you to add NYC to your personal profile. Knowing where someone is helps us give better help and hints because what works in one area may not in another and timing differs all round the world. Having a location in your profile saves us having to remember or keep scrolling back to the first post.