1.) Yes, a gnome can multi-class fighter and illusionist under the core 2e rules.
2.) Compared to ye-old-elven-figther/mage, its a weaker combo. Small size removes some excellent weapons, no elven chain for armor, and alot less spells to boot (no abure/invoc/necro).
If you plan on going this route, I suggest stocking up on misdirection and concealment spells (invisibility, displace self, mirror image) and get a short bow and hand-axes. You'll want mobility and range, as well as defense. A few non-evoc offensive spells (flame arrow, melf's acid arrow, burning hands) also do wonders.
Overall, the best choices for gnomes is illusionist/thief (stealth baby) or illusionist/cleric (esp of a stealthy/tricky specialy priest).