For many of these questions, you will get better answers in the Speedlight forum.
>1. How do I know if I'm in BL mode or not? Under what >conditions is it IMPORTANT to set, or not set, for BL?
I am not sure when the SB-800 is mounted on a D60, but when the SB-800 is mounted on other Nikon DSLR's with both the camera and the SB-800 On: check the Display on the SB-800, it should indicate: TTL, TTL BL, AA, or M modes. You can change the flash mode by pressing the mode button on the SB-800. The BL means the flash is optimized for Balanced filL flash. TTL BL is best used outdoors when you need some fill. When you are indoors or want the Flash to be the primary light source use TTL flash mode.
>2. I bought my SB800 used, with no manual. Can you give me a >link to one?
> Biggest question right now: Significance of mm >numbers 24 through 105?
Speedlight Zoom settings.
>Better Beamer says put setting on >"50"--why? If range to subject varies from 5 feet >to 75 feet, is 50 the best setting for all?
If they recommend using the 50mm zoom position, I suspect that the Better Beamer's optical design is optimized with the Speedlight zoom head set at 50mm.
>3. Many of my outdoor flash bird pictures are good. Some are >not. Biggest problem seems to be underexposing in low to >medium-low light. Setting is typically Aperture priority 7.1, >Better Beamer IN use (set at 50mm). Subject 15-25 feet away. >Some back light. What is problem?
There are several possible causes. Without seeing the image and the Exif data we can only guess. What Metering mode were you using? What Flash mode (TTL or TTL BL)? Was the Speedlight firing at full power (the ready light in the viewfinder and on the back of the Speedlight will blink when the Speedlight fires at full power)? The back lighting could be fooling the meter.
>How to correct? (If I >wanted to include a picture, with camera data available, how >do I do that?)
It depends on what the problem is. Download the image to your User Gallery and provide a link in your post.
>4. What is typical recycle time on SB800?
It depends on the type of batteries you have installed in the Speedlight and if you are using the 5th battery.
After a full power dump the SB-800 will recycle to full power between 2.9 sec. (w/5 fresh NiMh batteries) to 7.5 sec. (w/4 fresh Lithium batteries)
>How many flashes in 10 seconds before no flash occurs?
It depends on the number and type of batteries, how fresh they are, how much power the flash fires at, etc.... If the flash fires at very low power it can fire upto several times per second. If it fires at full power, you can get between 2 and 4 full power flashes in 10 seconds, again depending on the number and type of batteries.
>(By the way, if Flash is cycled-out, will the shutter still release, >so that I am unaware of just having shot "in the dark"?)
Unlike when using the built in Speedlight, when using the SB-800, the shutter will release before the Speedlight recycles to full power. Which will result in under exposure.
>5. I'm visiting the National Aviary in Pittsburgh in early >July. Typical large indoor environment, birds flying around, >some pretty far away. Will be using 300 F4, with 1.4 TC. Any >idea if using Better Beamer is better than plain SB800?
I suspect the Better Beamer would be the better option. That said, you might want to verify that flash photography is allowed. Good Luck and Enjoy your Nikons!