I fish the surf on the west coast of Florida.
Here's my take on your questions.

1) Spoons: mine are the "weedless" type. Is that also ok in the surf
Sure. You don't need the weed guards, but they won't hurt.

2) Spoons & weight: which size spoon should I choose? I mean - the
heavier, the further I can cast it, in particular in a windy day, but
heavier is also bigger, which might end up being too big for the fish.
The lures should be selected to match the rod you have. You want the whole
setup to be comfortable to use. You will be doing a lot of casting

Can I add weight to the leader by adding a couple of splint shot
sinkers or is the entire beach going to choke to death while laughing
at me :-)
Not a good idea. Use the right weight lure.

3) a little off-topic here, but I still want to ask you. Is is really
that bad to fish with a swivel/snap when using a lure? I use Yo-Zuri
and Rapala Original Floating lures and while I do notice a difference
in behavior (it takes less pull to have them go deeper) it is slight.
I was under the impression that the problem with a swivel/snap is that
it is too *visible* for the fish, but my (maybe mistaken) commen sense
tells me that a fish seeing a lure with a lure on leader with a
swivel/snap will think that the lure is "chasing" the rest of the
hardware, I mean - this is a fish, not a PhD student from MIT, I am
trying to catch - I am really mistaken here?

I use a snap swivel almost all the time. Those fish out there are predators.
They attack things that trigger some signal that says "eat that". If they
will attack a metal spoon, they will not be put off by a little extra metal.
I know that some will argue with that. Don't bother. I have discussed this
with several fish that I have landed and they agree with me.

On one hand, my only fishing book (-: unsurprizingly and adequately
called "Fishing for Dummies" :-) says that "some anglers use snaps for
changing lures or baits as well. This technique is a lazy person's way
out, and is definitely NOT the way to get the best action out of your
lure" while, on the other hand, local fishermen had told me that this
is simply "techno-snobism from purists" (and quote here). What do you
think?
PS: please let me know if I should maybe get another type of spoon/lure!

When you are out there fishing and some one is catching and you are not,
just go up to the guy or gal and after you say "Hi" ask " What are they
hitting today?" 99% of the folks out there will be happy to help.

Best of luck.

Charlie