If you're planning on a couple of days there, I'd stay on the Zim side for the reasons you've identified, as well there many more dining options (the food is MUCH better) and sporting/other activities is a bit easier.

Fy into VFA if possible (there is a BA flight from JNB in addition to the SAA flight daily...keep checking for space on the SAA flight often, it can change as tour operators hold and un-hold seats) it's a much easier and shorter option.

1) It's not difficult. The hotel you decide on should be able to recommend a tour company to assist with transfers (I've used Silver and Falcon Tours...both were fine: minibus..easy...$20-$30 each way....they will meet you at the airport and escort you all the way to your hotel). You can take a taxi...but you'll have to take one to the border...then one between the borders...and then another on the Zim side to your hotel. Border crossing are however, very easy (especially on land) and painless (just costly if you're North American). As has been mentioned, it is extremely easy to walk from Zimbabwe to Zambia and vice-versa.

1a) YES!!!

2) Get a multiple if you land in Zam.

3) Doesn't matter....both are just one border crossing.