I know this is an old post, but I thought I could add a bit of info for anyone else who may be considering dropping a Uno Turbo engine into a Tipo.
First of all, it should be a fairly simple swap dropping in the Uno Turbo engine in place of a Tipo unit. The 1.4 Tipo engine is the same as the 1.4 Uno engine, and this is also the same basic engine that the Turbo engine is based on. I'm not 100% sure, but I also think that the 1.6 Tipo engine is the same basic block as the 1.4/ 1.3/ 1.1 (non FIRE) engines as well.
However, the 2.0 16 valve Tipo version has an entirely different engine so wouldn't make a very base for a turbo swap, even though it would already have uprated suspension and brakes etc.
Gearboxes:
Probably best to use the Tipo gearbox, and later Uno's (turbos included) used a Tipo based gearbox anyway. Seeing as yours is a 1.6 it is designed to handle extra torque, so as long as you aren't too wild with the throttle it should cope fine with the Turbo 1.4. You may find the gear ratios aren't perfect, but a check in the Haynes manual should show you the ratios of both the Tipo 1.6 and also the Uno Turbo boxes. They probably won't be that different, though the Tipo may have a higher final drive ratio.
Another good reason to use the Tipo 'box is that you know there won't be any problems with gearchange linkages or driveshafts. Also, it will allow you to keep the electronic sender wired to your digital dashboard/ speedometer, though I see no reason why this can't be swapped from the Tipo 'box to a Uno 'box.
The turbo driveshafts differ from standard Uno driveshafts on the drivers side. Here a two piece drive shaft is used in an effort to combat torque steer. All other models used a single piece shaft. On the Tipo I don't know if a two piece draft shaft was used, but there doesn't seem to be any reason for not using the standard Tipo shafts. You might just have to put up with a bit of torque steer but hey, you can't have everything!
Alternatively, look up the driveshafts fitted to a 2.0 16 valve model. This engine pushes out nearly 150bhp, so maybe you could use the driveshafts from this model? They would be more than capable of handling the power from a 1.4 turbo.
Another area needing looking at is the brakes. The turbo uses discs all round with ventilated at the front. It might be possible to swap the fronts over, but I'm not sure about the backs. Saying that though, disc brakes at the back are not that necessary, seeing as even basic drum braked Uno's had a brake proportioning valve to stop the rears from locking! You'll probably find the Tipo has a load proportioning valve too for the rear brakes.
The exhaust shouldn't be too difficult to solve seeing as most of the turbo stuff is contained within the down pipe area. You may find the turbo downpipe will hook up to the rest of the Tipo exhaust. The only problem might be that the Tipo exhaust won't work well with a turbo application.
The biggest problem is going to be hooking up all the electrics, sensors, turbo engine wiring loom and ECU's. Somehow you will have to incoporate this into the Tipo's wiring loom. It's possible, but might need some planning and an auto electrician to make sure that everything is connected as it should be. Also bear in mind that you will need things like intercoolers, oil coolers, electric fuel pumps and regulators incorporated into the Tipo's body shell.
There seems no reason why all this can't be done to make a Tipo Turbo, BUT, I would have to ask if it is worth it? The basic engine swap should present no real problems, but incorporating all the additional turbo ancilleries and electrics might well be one big headache. You will also have the problem of insurance, as the car will be seen as heavily 'modified' and not a standard car. This could well send the insurance premium through the roof.
Seeing as some very nice Uno's are still around for just a few hundred pounds, I would be more tempted to buy one of these and effectively 'reshell' your rusted turbo. That way you can swap everything over and it should all fit with no problems. The basic Uno bodyshell is pretty much the same as the turbo!
If you did re-shell you would then have to re-register the log book as a turbo, but for all intents and purposes the car will be a standard Uno turbo after that so it shouldn't affect the insurance. Of course, there is also nothing to stop you from swapping over the chassis plates and using the original number plates from the rusted Uno, only that is a bit naughty! If you do this make sure you send the log book off and register the new colour to avoid any confusion from the boys in blue. Also remember that some of the chassis details are actually stamped onto the offside suspension turret, and that isn't easy to change. Still, with an angle grinder and a bit of filler and paint who's to know if it was ever there? Not that I condone doing this kind of practice (ahem!)
Remember that all cars have their details on a central database. So if you have simply reshelled into another Uno without changing the details, then you are stopped by the police and they do a chassis number check you might have to explain why your Turbo is actually registered as a 60S!
Even though your Tipo is mint, I'd be more tempted to sell if for more than you paid, then use that money to hunt down a good Uno with a sound body to re-shell your rusted Turbo. At the end of the day it would make life much easier!