While intermediate and advanced cider-making is a bit different, the following is for basic ...
>> Is my next transfer into bottles or into another carboy?
Into another carboy. This allows the spent yeast that has already fallen to the bottom of the first carboy to be separated-out by siphoning or 'racking' the clear cider off-of the powdery layer of sediment on the bottom.
Then the cider will sit in that final/second carboy to wait for the ferment to absolutely finish and the cider to clear completely by letting all the yeast fall to the bottom. Then you will transfer to bottles.
>> How will I know when to make that transfer?
Transferring to that final/second carboy is done when the fermentation substantially subsides, and the airlock passes a bubble only occasionally (say one bubble every minute or so, it's not an exact number), and the suspended particles in the cider fall the the bottom so the cider now looks more clear ... then you transfer to the final/second carboy.
Some people don't transfer to that final carboy and instead let the fermentation completely finish in the existing (first) carboy and then bottle. That is possible too, though it often is less desireable to do it that way.
Benefit of *not* using the second/final carboy ...
you don't expose the cider to as much oxygen because racking always introduces a bit of oxygen (and sometimes, microbial) exposure.
Benefit of *using* the second/final carboy...
If you do not use that final/second carboy and instead let it sit in the first carboy, because you will be letting the cider 'sit' on the 'lees' (the dead yeast at the bottom of the carboy), you can end up with a usually unintended condition called autolysis which causes a continued slight bubbling and some other chemical changes. The dead yeast at the bottom of the carboy cause a re-introduction of a slight amount of nutrients and so the live yeast feed on the dead yeast. This increases the chance of unintended chemical activity ... this can cause undesireable changes to the flavor profile of your cider. It doesn't always happen, but it is a possibility. In advanced cider making you might utilize that autolysis for positive purposes, but for a beginner, separating the cider from the lees/sediment at the bottom of the first carboy is preferred ... and is done at about the time when there is only a very occasional bubble in the airlock.
Bottom line ... if you have a racking cane and proper tubing to rack with, I'd recommend using that final/second carboy.
Once in the final carboy you can let the cider absolutely finish fermentation and sit there and clear further for varying amounts of time, but for our purposes let's say 2 weeks to a couple months (depending on clearing) ... then bottle.
Like I say, using a hydrometer prior to bottling is the preferable way to determine that the fermentation will not continue.
(Note that it does not mean that the yeast are all "dead" ... they are just not active ... if you added sugar, they would start back up again)
At the time of bottling, usually you would use a hydrometer to measure the amount of sugar still in the cider as a way of determining how completed the fermentation is. You want your hydrometer to read 1.000 or less to show there is no more fermentable sugars.
This is what tells you that you will certainly not create a batch of hand grenades.
>> I was planning on sterilizing and reusing the 1L screw top glass bottles the juice had originally come in, is that a reasonable choice?
No. For sparkling/carbonated cider I would only use bottles that were originally used for pressurized, sparkling beverages ... beer bottles, pop bottles, sparkling wine bottles etc.
For "still wine" (not carbonated) cider you can use whatever you'd like.
Generally, screw tops are not preferrable if you plan to hold the cider for more than a month or two because they can leak in just a little bit of air/oxygen. However for a small first batch, screw tops will be fine. In fact, just to make things easy on themselves, some vintners just put the sparkling/carbonated cider or wine into screw top plastic pop bottles, and then just store it in the bottom shelf of the refrigerator to arrest/prevent any further unintended fermentation.
Sparkling wine and cider can go shockingly fast and that method is convenient for beverages that will not be around long.
The preferable closure/capping for bottled sparkling beverages is to use either beer bottles & caps (and a cap press) ... or possibly the type of 'swing-closure' that you can see on the top of Grolsch Beer bottles ... or even sparkling wine bottles and corks.
I am personally fond of using 22oz capped Guinness beer bottles when I make cider.
>>If I'm trying to make some bottles carbonated using priming sugar, how do I make sure the bottles don't explode?
By very carefully measuring your priming sugar. Read up on the process. Do the math carefully and measure carefully.
Many people will also halt any unintended pressurization by pasteurizing the cider using a hot water bath after they've added the priming sugar and the final "carbonating" fermentation is done. There is quite a bit of good info on HBT about how to pasteurize bottles.
FWIW ... pasteurization is also one the methods used to make carbonated hard cider which is also sweet (still has some sugar in it).
>> I'm nervous about trying to bottle too soon and there being too much active fermentation and creating bombs on accident.
Use the hydrometer to determine if there is still enough sugar in the cider to cause continued pressure buildup.
Furthermore ... Keeping your cider bottles on the bottom shelf of the fridge is a convenient way to make sure you don't have further pressurization.
Out of a batch of 25 bottles, store 20 in the refrigerator, and take say, 5 random bottles and put them wrapped in heavy towels out in the garage or basement at room temperature (or somewhere you won't have a problem with a floor full of cider), and open one periodically ... say one at the end of week1 ... week 2 ... week 3 etc. If one or more spooze like crazy and shoot all over the place, you may be over-pressurizing ... and you'd probably be best to keep all the cider in the icebox.
>> In general, if something else is added to cider in the secondary ferment (like fruit mash/pieces/juice), is there a need to move the cider off the residue a second time?
Things like fruit or raisins etc are added in the 'fermentation bucket' ... generally you will rack the cider off of all that stuff as you put it into the first carboy ... and certainly by the time you rack out of the final/second carboy (and put to bottles), any remaining particles should have fallen out of the cider and be at the bottom of the final/second carboy by the time you bottle.
When you first begin making cider, beer or wine, reading at great length on HBT is time well spent. All the things I've mentioned above have much greater detail and information if you take the time to really research each aspect.
Also ... is is important you keep very accurate notes so that your future vinting (or brewing) is more successful and goes smoother.