Ceiling – suspended ceiling tile that allows sound to pass through without reflecting sound

If sound proofing is your primary concern then you should build the walls all the way up to the roof, past the suspended ceiling. You should insulate the walls with sound-dampening insulation. If you are willing to spend more money and time, you should look into isolating channels that the drywall attaches to. This prevents sound from being carried through the walls and studs (normally sound hits drywall and vibrations are carried through the studs to the other side. The isolating channels prevent this).

I do not think a suspended ceiling will be able to hold the weight of the insulation. As well, usually a big benefit of a suspended ceiling is easy access to the plenum space above for running wires, accessing hvac/plumbing/fire equiptment, etc. If you have insulation on top, everytime you need to take a panel out, you'd also have to take out a lot of insulation. It would also be hard to get it back in properly after removing only a single tile. The tiles themselves should help eliminate the echo.

The insulated partition wall is the primary means of attenuating sound transmission. The adjacent concrete structure provides a flanking path for sound to travel around the edges of the partition, so sound needs to be prevented from reaching the concrete. Normally, one only needs to insulate about 5 feet from either side of the partition to mitigate flanking paths. Due to reverb problems, insulating the entire area could be warranted.

Despite all the added insulation, you will still have reverb problems unless the new finished surfaces are selected carefully. Don't forget the floor can also be a flanking path. Carpet and padding will help. Saw cutting the floor slab under the partitions would also eliminate the flanking path, but could cause other problems if the sub-grade is unstable, so consider this approach carefully.