Can multiple versions of the same package co-exist on the same system?

No, it is not possible to have two versions of the same package, because there will be conflicting files. If a library is capable of being installed in two different versions at the same time is a different matter. If you're brave, you could get the source code for one version and see if you can install that to a different directory. This could very well mess up your system in nasty ways. It could also just plain not work. Dpkg won't be satisfied, so you'll have to get the source for one of the programs and compile that too. But bear in mind that once you start compiling programs yourself, you can cause yourself all kinds of problems.

No, you can not have different versions of the same package installed at the same time. Usually dependencies are expressed as at least version X. For packages that are all built from the same source however, the dependency is often exact. This is what you have run into. libncurses5 and libtinfo5 are both built from the ncurses source package. If you want to upgrade one of the packages built from this source, you must upgrade all of them, so you simply need to get and install the same version of the other packages built from this source, so they are all on the same version.