Traditionally, evening attire breaks down like this.
>> "Formal" = "Black Tie" (tuxedo or dinner jacket for gentlemen, and evening gown for ladies)
>> "Semiformal" = Formal business attire (business suit for gentlemen and either business suit, business dress, or fancy cocktail dress for ladies)
>> "Informal" = Standard business attire (sport coat, slacks, dress shirt, and tie for gentlemen and a business dress or cocktail dress for ladies)
>> "Casual" = Shirt with collar and slacks for gentlemen (sport coat optional) and either blouse and skirt or pants or cocktail dress for ladies)
The distinction between "semiformal" and "informal" has become blurred in recent years and the cruise lines modified the definition of "formal" somewhat (to admit a dark business suit for gentlemen as an accommodation to the fact that, about thirty years ago, most gentlemen did not own tuxedos or dinner jackets), but the distinction between "casual" and "informal" or "semiformal" is still pretty clear.
Celebrity also has a reputation for being quite "upscale" -- more "upscale" than the other "premium" cruise lines generally regarded as its direct competitors. If in doubt, you probably will be much less embarassed if you err on the formal side than if you err on the casual side.
Now, to answer your questions:
1) What would be examples of informal dress? Would it be along the lines of what you'd wear to a wedding, or is that too fancy?
What you would wear to a wedding definitely would not be too fancy for an "informal" night. A dress shirt, necktie, dress slacks, sport coat, and dress shoes are the minimum for gentlemen. For ladies, a cocktail dress certainly would be a safe choice.
2) Would a nice pant suit be appropriate informal wear for a woman, or should slacks be reserved strictly for the casual nights?
A women's business suit with pants would be okay. OTOH, this is much more of a social occasion so a cocktail dress probably would be a better choice.
3) Right now, we're feeling like we need to pack half our closet for this trip. Not a problem, except for the airline weight limitations on baggage. :-) Would it be a faux paux (sp?) to wear the same thing to dinner two nights? (E.g., wear the same formal outfit to both formal nights and the same informal outfit to the informal nights?)
The two formal nights are far enough apart so wearing the same basic outfit should not be a problem, but you might want to pick different accessories to produce a different look. For gentlemen, many tuxedo companies offer cruise rental packages that include two shirts (with studs and cuff links), a vest with a matching bow tie, and a cummerbund with a matching bow tie so the tuxedo or dinner jacket does not look quite the same. For ladies, a popular strategy is to bring a formal dress with a couple different sets of accessories that coordinate with it but that give it different looks.
We love dressing up and would like to take separate outfits for each night, but we're just not sure there will be enough room in our suitcases.
You really need not take "half your closet" if you think strategically when you pack. By way of example, I usually forego T shirts and bring knit "golf" or "polo" shirts instead. These shirts are casual enough to wear for daytime activities (sightseeing, around the pool, etc.) but still dressy enough to wear to dinner on casual evenings. I also bring pants and shorts that will coordinate with several shirts, so three or four pairs of each are sufficient for the whole cruise -- and the pants that I bring are dress slacks, so they are acceptable for sightseeing in cooler (Alaska) or more formal (Europe) destinations, but also appropriate for wear to diiner -- either with a dress shirt, a necktie, and a sportcoat on semiformal evenings or with a "polo" or "golf" shirt on casual evenings. By choosing items that provide this sort of versatility, one can pack a lot fewer items. Also, one can choose evening outfits that coordinate with one or two pairs of dress shoes, evening purses, etc., so one does not need to bring a separate pair of dress shoes for each outfit.
The other trick to reducing your luggage is to think strategically about what styles of clothing you are bringing. By way of example, a formal cocktail dress will require a lot less space than an evening gown. Likewise, a women's bikini swimsuit or a men's "speedo" may fold into a lot less volume than a traditional women's "tank" swimsuit or the "boxer" style men's swimsuits that are in style today. Certain styles of underwear also fold into a much smaller volumes than others -- and nobody aboard ship will know what style of underwear you are wearing, so it really does not matter. It's even possible to bring jewelry that you can wear with two or three outfits, or that you can wear sightseeing as well as in the evening, to minimize the amount of "stuff" that you have to lug. These savings also cut down on weight, so you'll have some reserves for souvenirs on the return trip!
BTW, the weight should not be a problem. On my last vacation, I took enough clean clothes and toiletries for seventeen days -- including a ten-day cruise with two formal nights -- in two suit cases, one of which was small enough to carry on, and had no problem with weight limits.
Have a great cruise!