I've just noticed I'm not fully patched to 1.12. I'm going to do that
now and see if that helps any. Maybe the Necro's were improved in the
patch.

Andariel is always a bit of a pain because you're relativaly low level
when you reach her, and she has a nasty poison cloud attack, which also is
quite damaging to your skellies. However, just go somewhere else (use the
WPs you have) and re-collect an army, then return via the TP to her. Redo
this a few times, and you should be able to get her.

If not, just restart a game, and try to gain a level or so, and put that
in RS.

Yes, a build as described in your link will work fine. Although I would
ignore the bit about wearing Guillaume's Face and/or using a Stormshield.
The only Str related bit is if you want to use Marrowalks, since these
need a bit of Str. However, these are not really necessary.

Nothing, except perhaps reaching Andariel too soon. You will run into a
few more of these encounters in Normal difficulty (especially Normal
Diablo is a pretty tough cookie for a Necromancer below clvl30), but NM
should be a walk in the park, and in Hell the only places where you'll run
into trouble are in Act 2: The Maggot Lair and Arcane Sanctuary.

There are more things to watch out for in Hell, most importantly Gloams,
but that's also why you should aim for maxing you Lightning Resists first,
so they pose less of a threat.

As for your own follow-up post: what version of Diablo II were you using
if it wasn't for 1.12?

Regards,

Patrick.