It's possible to achieve the goals, but the system does need some equipment that will allow this. The one dimension I don't see is the height and it's one of the more important factors.
You want the speakers to be as close to the people as possible, to prevent the need for excessive SPL and the associated echo that would result. You also need to use more speakers and since this place is used for getting people pumped up to dance & move around, sound quality isn't as important as it would be in a theater or someplace that hosts speaking engagements, although speech intelligibility is still important. That's why many speakers and lower SPL are important.
In-ceiling speakers can work for a place like this, but you'll need to use some kind of subwoofer(s) to handle the bass frequencies- whether the sub(s) are on a wall-mounted bracket or in the ceiling, they need to cover some bass, but it's not important to go much below 40Hz and you'd be better off with good mid-bass rather than worrying about the lowest octave. Also, you don't need stereo separation, you need coverage, so plan on operating this system in monoaural.
Power amps and small mixers can be fairly inexpensive, but I don't know all of the products that are available in your part of the World, so I'll mention some brands and details that worked for me last year when I installed equipment for an exercise/fitness facility that has a main room (about 40' x 60', 14' high) and a yoga studio (22'x 35', 14' high). We haven't done anything about outdoor speakers at this point, but I suspect it will happen at some point.
-Sources- Bluetooth receiver for smart phones/tablets
-Cable with 3.5mm plugs for same, if they don't have Bluetooth
-Wireless Mic (the owner had a Radio Shack setup that didn't work at the previous place, but it has worked well at the new one- I suspect it was made by Audio-Technica or Sampson)
-RCA input from other mixer outputs, in case they want the same program material playing in all areas
-One additional channel open, for future use
Speakers-
-One pair of Polk Atrium 6 indoor/outdoor speakers in the yoga studio
-4 pairs of Proficient 8" in-ceiling speakers in the main room, which has three I-beams for support, creating four sections in the ceiling
-One JBL Control Sub200 subwoofer in the main room
Power amplifiers- one Behringer A500, bridged, for the subwoofer
Dayton Audio 12 channel x 45W amplifier for the in-ceiling speakers (using one channel per speaker and each pair of two channels bridged for the Polk speakers)
Audio Processors-
-Rolls mixers (one for the main room, one for the yoga studio), 5 channel with two mic inputs
-Art Audio Head Amp, used to allow the mixer output to be sent to four pairs of amplifier channels, in case the level needs to be adjusted in the four zones of the Main room
-Behringer EFB-1500 equalizer/crossover- since the rooms are in mono, one channel was used for each, adjusted for the needs of each room The High Pass and Low Pass settings allow for higher output without problems with bass frequency handling with small woofers and the Low pass only feeds the JBL subwoofer.
I had a tight budget, so I found equipment that was pre-owned, but I knew its history (I had installed it all for other people and both bars had closed or changed hands, so I knew it was available. The speakers, mixers, Bluetooth receivers and Head Amp were new). I was pleasantly surprised by the Proficient speakers- I had heard them in the displays at my suppliers, but hadn't used them before- the sound was more full than I expected. They don't handle strong bass, but they do well with the bass removed (below 45-60Hz). I set the crossover higher because there's no reason to try to make them do something they can't.
This place rocks. I don't listen to Rap or Hip Hop, but I know how to make a system perform for that and when I initially turned the amp on for the sub as the owner's father played some of his music, he just started to laugh- it really does a great job, even when people are working out, outdoors.
It's more important to limit the signal to the speakers, use one moderate-output channel for each speaker and set the levels appropriately than to use one extremely high powered amplifier for each zone/room. That's a much more expensive method and it will cause more problems than it solves. High volume levels causes echo, low volume is much more manageable. You won't have people being blasted by one big box firing over their heads, just so the people in the middle can feel the music. With more speakers, the room will have no dead spots.