To install a toilet that doesn't need to have a drain pipe coming out underneath is quite easy. You have to chose the right toilet.
The right toilet will have a "rear discharge". It will either 1.) hang on an in-wall carrier, or 2.) rest on the floor like a regular toilet.
I'll take a minute to describe the big picture first, OK?
It is not good to choose a regular toilet and then raise it onto a platform or raise the whole floor. That is because of the danger of tripping or falling when stepping up and down, because the height is a single full step.
(There is one exception to this statement.) Some toilets designed for basements have a 3"height flat storage tank built underneath them and then the waste is pumped up a few feet to reach the house drain. These work well, since the raised part is designed
low enough and far enough back that nobody is required to step up onto it to get seated on the toilet. It raises the toilet seat to the same height as an ADA toilet made for wheelchair people. Most people prefer the seat to be higher than the average toilet is at anyways. And those who would like to have the floor closer to the seat can still place their feet on the 3 1/2" - 4" finished floor on top of the flat storage tank which comes just far enough forward to be comfortable to rest your feet on too. (I have seen all this first-hand being built but was not the primary DIY in this case.)
However, that option is not recommended to you in a condo. A pump will always make noise, and the noise will always be associated with raw sewage so it will have negative psychology too.
Rear discharge toilets are rare animals but do exist in limited numbers. They are used in condo buildings and in other situations where the right way to connect to the main drain is to send the toilet discharge out the back or to the side.
Some are floor-mount; some are wall-hung. I have not seen any floor-mount rear-discharge that I know of; I have seen many wall-hung, and installed a couple too, after months of planning.
Wall-hung toilets are cool and look cool. Designers like them. They free up the floor. There are many types of carriers, and even more models of porcelain bowls to fit on one or another carrier. Some are American. Some are European.
Some are Japanese.
Some are Turkish.
Some are Australian.
They all have US offices and have gotten the approvals to sell their toilets, so nothing is experimental or "at your risk", at least not more than any other design of toilet.
Even in a regular type of house you can see the need for a rear-discharge occasionally. See
https://terrylove.com/forums/showthread.php?t=10698 about toilets that can send their discharge sideways out the back.
Also
https://terrylove.com/forums/showthread.php?t=10623 is a new thread with only one post so far. It is a good start, showing a lot of options, but not all. The last photo in Post #1 is of a flushvalve toilet; these are WAY too noisy for a condo in a multistory building. Maybe even in a townhouse condo. Your building may be made of concrete. If so, you have natural soundproofing since concrete dampens outdoor noises (like wind) and indoor noises too. So you are in a very quiet environment, and a flushvalve would sound dramatically noisier since your baseline background noise is so low to start with.
That is the big picture. In your case, nothing is clear yet, because it all depends on your building's plumbing. How you will connect the discharge is not clear yet -- you have to tell us more about the plumbing in your building. You cannot connect it to the existing toilet. There is no advantage for a wall-hung toilet to be positioned directly behind an existing toilet whose discharge goes down through the floor, and no you cannot tie into that pipe.
As a condo owner you have the absolute right to know what your plumbing is, everywhere in the buiding in the co-owned parts which includes necessarily the building's "stack", i.e. main drain which starts at your floor. You have the absolute right to have access to your plumbing too, and your downstairs neighbor has the same right for his plumbing...
2.) Waiting for Hot Water.
See
https://terrylove.com/forums/showthread.php?t=10731 "Instant hot water at the tap. Cheap, fast, efficient." about ways to get the hot water you need right away. Post more there too. Or here.
hope this helps.
-david