I have this Juniper nana I bought a couple of weeks ago, I've been letting
it adjust to the temperature here(and because it was shipped)

The name is Juniperus procumbens 'Nana,' or dwarf Japanese juniper.
Where is "here?" I hope you are keeping it outdoors where it belongs,
preferably iin the sun.

I'll be ready to prune probably next week

Why? What makes you think it needs pruning that urgently? Let it become
accustomed to your location first.

The tree is a bit weird I think.

What is weird about it? Junipers are suitable for all sorts of fanciful shapes.

1)should I tell the guy where I bought the plant that I'd like to buy some
soil from him, since my juniper is already used to it?

If the tree has been repotted recently, you won't need more soil for a couple
of years. By then, you may find some you like better.

2) Should I protect against pests, and if so, with what?

keep a watchful eye, & only spray if you actually see mites or insects. I
happen to prefer Orthenex, but you can only use it outdoors or in the garage.

3)my nephew decided to go digging in the gallon bucket the bonsai is in, and
a little soil got missing,

Gallon bucket? So this is a starter plant. Unless the trunk is already thick,
you might do well to plant the tree in the ground for a few years.
Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)