There is no problem with installing junction boxes above a suspended ceiling, as long as the box is less than 100 in.³ and securely fastened. National Electrical Code has this to say...
National Electrical Code 2014
Chapter 3 Wiring Methods and Materials
Article 314 Outlet, Device, Pull, and Junction Boxes; Conduit Bodies; Fittings; and Handhole Enclosures
II. Installation
314.23 Supports. Enclosures within the scope of this article shall be supported in accordance with one or more of the provisions in 314.23(A) through (H).
(D) Suspended Ceilings. An enclosure mounted to structural or supporting elements of a suspended ceiling shall be not more than 1650 cm3 (100 in.3) in size and shall be securely fastened in place in accordance with either (D)(1) or (D)(2).
(1) Framing Members. An enclosure shall be fastened to the framing members by mechanical means such as bolts, screws, or rivets, or by the use of clips or other securing means identified for use with the type of ceiling framing member(s) and enclosure(s) employed. The framing members shall be adequately supported and securely fastened to each other and to the building structure.
(2) Support Wires. The installation shall comply with the provisions of 300.11(A). The enclosure shall be secured, using methods identified for the purpose, to ceiling support wire(s), including any additional support wire(s) installed for that purpose. Support wire(s) used for enclosure support shall be fastened at each end so as to be taut within the ceiling cavity.
Code Violations
In the first image, the wires being spliced together like that violates NEC 300.15.
300.15 Boxes, Conduit Bodies, or Fittings Where Required. ... Where the wiring method is conduit, tubing, Type AC cable, Type MC cable, Type MI cable, nonmetallic-sheathed cable, or other cables, a box or conduit body shall be installed at each conductor splice point, outlet point, switch point, junction point, termination point, or pull point...
I've also noted some violations in the second image.
Click for larger view
You might not have to create a fully vertical face to apply your crown. Crown molding is usually either 38 or 45 degrees (with some exceptions, so make sure and check) and it looks like the wall angle is greater than that so all you need to do is create a flat spot for the foot of the crown to land on. Here's a drawing:
I wouldn't recommend 1/4 round because it always looks like you're trying to fix a mistake and it shows all the inconsistencies in the wall/ceiling. Hope this helps.
Best Answer
It looks like water damage to me. Likely either a roof leak or a condensation problem with one of the ducts (or something else entirely that you don't know is there?). It's also possible for the leak to be elsewhere above the ducts and this is just where the water found its way down to the ceiling.
Do you have access to the area above(attic)? If so, maybe a couple pics of what's there might help.
Also, you can buy a moisture tester help diagnose this. If the ceiling at the stain is the same moisture content as surrounding ceiling, then the problem isn't currently happening but that doesn't mean it won't come back. If it gets wetter during or immediately following a storm that almost guarantees a roof problem.