Splicing wires in a big box
Yes, that's fine.  I do it myself.  I bought some 10x10x6 boxes for splicing some wires that had been cut short by copper thieves, and also to house relays for some lights.  

You can also connect the box(es) to the service panel by lengths of EMT conduit (which is exactly what I do). This takes care of grounding.  You are only allowed 4 circuits per conduit (unless the conduit is &lt;24" long), so in the case of my big 6x10x10 box, I ran 4-6 conduits between box and panel.  

For simpler jobs, my preference is to run a 1/2" or 3/4" conduit to either a 4" or 4-11/16" square junction box (much cheaper at the electrical supply than the big-box store).  Then I bring 4 circuits into each box.  For the last hop from box to panel I use stranded THWN-2 individual wires, which is easier to work with and is legal in conduit.  (the reason not to use stranded THWN everywhere is it's hard to attach to receptacle/switch screws, until you get the knack).  

These boxes are also nice places to mount GFCI deadface or receptacles if you want to protect a whole circuit, but don't want to spend $40 for a GFCI breaker. 

You need 4-1/2 cubic inches per pair of non-ground wires spliced.  So one 120V circuit needs 9 cubic inches, and a 120/240 split phase circuit needs 13.5 c.i.  You also need one 2.25 cubic inch allowance which covers all ground wires.  I use  4-11/16" boxes (or 4" square boxes with extension boxes) for the necessary cubic inches; (42 c.i. and 22+22 c.i. respectively).