How important is case trim length?

Case length does not affect powder capacity, at least not that it can be "remedied/restored" by trimming. Case neck holds bullet, not powder. The only reason to trim is to assure that brass has not moved into neck pushing neck length beyond the chamber dimension.

In this regard, is Case trimming necessary?

There is no set rule as to how often cases should be trimmed to length. Some calibres will need trimming more frequently than others. If you are using a 'pokey' load, and by that I mean a load that is near the top end of the pressure range, brass tends to flow more and so the cases will need trimming sooner.

Beside above, do you trim cases before or after resizing? The main reason for trimming is so your case isn't too long for your chamber. There is "1" exception. That is if you're using the X-Dies. In that case you trim once before sizing and then you never trim again.

Likewise, what is case trim length?

The "trim to" length is the length of the case only. Max length is the maximum length of the assembled round. In a . 45 ACP it's about 1.250 inches and a . 223 is about 2.26 inches.

Does once fired brass need to be trimmed?

If the cases measure less than the maximum, trimming is not necessary. Measuring is a must, though, which you did, tkill. To be safe, don't assume once fired rifle brass (or twice fired, three times, etc.) does not need trimming at each reloading cycle.

What length should I cut .223 brass?

The Max case length for the 223 is 1.760 inches. The trim to length is 1.750 inches. If you actually trimmed your brass to 1.45-1.50 you would have no neck left. The junction between the shoulder and the neck measures 1.557 inches.

Do you anneal before or after resizing?

You should anneal before sizing. Work hardened brass "springs" back more after the expander ball opens up the neck. Annealing before sizing help ensure more consistent neck tension.

Do you have to resize brass every time?

When you resize a piece of bottlenecked rifle cartridge brass, you definitely need to lubricate it first. One partial exception is case neck resizing. While outside the scope of this article, if you intend to use your cartridges in the same rifle, every time, you don't need to resize the full case.