First off, welcome to TeamCapri!
The linkage is likely due to worn shifter & linkage bushings. This is a common but easily fixed issue
Regarding the turbo "swap": You *could* put a turbo motor in with your existing trans, yes it'll bolt up, but the stock N/A trans isn't built for the torque(the XR2 has a stronger transmission and axles designed to minimize torque steer). Especially if you plan on pushing more boost.
The bare minimum you'd need:
Turbo, turbo manifold, injectors, VAF, engine harness, distributor, knock box, and some sort of intercooler either OEM or aftermarket. And probably a good aftermarket clutch
There's a search function on this forum, the turbo conversion has been discussed plenty. I have performed it before, it's involved but do-able. But you basically need an entire XR2 as a donor to "do it right" so the whole "Is it worth it, or should I just buy an XR2?" issue comes into play.
Happy to answer any questions regarding it