Are my wires in this junction box too short?
The work is solid with a few exceptions.  

Yes, that's too short.  You should be leaving 9-12 inches.  The legal minimum is 6" past the clamp, or able to reach 3" beyond the finished wall surface.  It can seem cluttery, but cluttery is good.  

Are you using a book on electrical?  The book would tell you this. People learning electrical work best when they have a general overview of all aspects - a primer if you will. Google can't substitute because Google only answers questions, and without a well rounded set of concepts, it's hard to know all the questions  you should be asking.

You will need to replace all three legs, and you will be better off doing it now, rather than waiting until the drywall is up, you are doing any kind of maintenance, and you are forced to improvise.  Remove the old cables carefully and you can reuse them - maybe even for each other.  

These push connectors are particularly problematic with short wires, because it is annoying/difficult to wrest the wires out of the push connectors, so people usually just snip them.   You'll want even more length for that. 

Some people get snipper-happy and go out of their way to cut wires as short as they can.  Perhaps they think there are brownie points for that... Code does mention "neat and workmanlike", but functionality and maintainability come  before neatness. Another trouble spot is the panel - it's in vogue to go snip-snip*, but for maintainability, you should give every circuit enough length so both hot and neutral can reach every breaker position in the box.  



You need to ground the box also.  Most boxes have a threaded 10-32 hole in the back for a ground screw. Some are on dimples so they work flush against a surface, look for that feature in boxes.  They sell special green #10-32 ground screws.  But any will do.  Do not use a deck screw or sheetmetal screw unless it is cut -32 thread or finer.  

Rather than spend a big budget on connectors, I would recommend using wire nuts instead.  Not least because you can take apart wire nuts and reassemble them.  But even more, because wire nuts produce reliable connections, and push connectors - like any backstab - are notorious for series arcing and failure.  At least you are in a metal box, which will contain all but the worst series arcing.



I also see where you have knocked out two additional knockouts.  You need to fill those with knockout plugs. Those are trivial cost, about a buck for five.  Alternately, if you are expecting more cables to come in, you are painted into a corner with those push connectors. 

Assuming you'll have 5 cables, it's time to start talking about box fill.  If the box is getting too crowded, you can get either box extensions or "mud rings" which provide some additional cubic inches.  On the Web there are "official" tables and calcs for box fill, but if  you are leaving yourself 9-12" of wire, you'll know when boxes are getting crowded.  The takeaway is that extensions (and larger boxes) are available. 

My signature box when I have >5 cables converging is the 4-11/16 square x 2-1/8 (120 x 55mm) which I buy at electrical supply houses, where they are much cheaper. 



* check out this disaster of a box.  Looks purdy, but now add a generator interlock and a whole house surge suppressor: those need to go on top, so every breaker must move down 2 spaces.  That expensive subpanel cable definitely will not reach, ouch!  And then, when they add GFCI or AFCI to some breakers, none of the neutrals can reach.  But he leaves lots of slack for the short service line (why?) Also, the panel is completely full, so it was a poor choice.