Hooked battery wrong way
If you hooked the battery up backwards then you likely smoked the fuse links at the starter solinoid on the inner fender passenger side. but it likely id the alternator was smoking then you likely smoked it as well. Start by checking all the fuse links at the starter solenoid, and im sure you burnt one or 2 . Replace them and the alternator.
Check fuses..... Fusible links....... once you get the power back, watch your alternator, theres a chance hooking power leads up backwards can kill the Alternator.
Reversing the battery connections is not too uncommon. If the key is off the damage is often just fusible links and fuses and the alternator. If, however, the key is on a great deal of damage can be done. Many relays, the computer, the ignition switch, etc. If the starter was engaged, it too might have been damaged. And there is the possibility that wires, anywhere in the harnesses, have damaged insulation but won't short out until some future time.
There are "wires" in the engine bay that are designed to open up in an over-current situation. They are called fusible links. The car also has fuses on all of the electrical circuits to protect the wiring from burning up in the event of an over-current situation. So, the polarity reversal may have resulted in one or more fusible links and/or fuses blowing to protect the wiring. The wires themselves do not care about polarity so the likelyhood of any additional wiring harness wires being "fried" is remote.
What can happen is that any electrical device on the power bus may have been compromised. For example, your radio is likely to not only have a fuse on the general circuit feeding it and other compoenents, but also an internal fuse to protect the wires feeding just the radio. Sometimes, they do not even have fuses internally but some electrical component on the power supply front end is sacrificed so the radio becomes inoperative. If your radio is dead, it needs to be repaired or replaced (assuming the general circuit fuse is OK).
With regard to the longer cranking times, it's probably a result of the battery power being removed from the ECM and so it lost all of the memory stores for operating parameters. It has to re-learn over time and use to custom tailor the controls to the engine condition. The older the engine, the more likely it requires some custom settings to operate best since it no longer matches the performance of a new engine. If the ECM is doing its job, it's probably fine and in time, it will adjust to the settings necessary to operate as it did prior to the battery swap.