Money Dance is not cloud-based, but everything is retained on my personal computer
You are correct. The data stays on your local hard drive. If you decide to sync your data with another machine then a cloud-based encrypted intermediary folder is used.
Can I enter split transactions?
Yes. Moneydance can create split transactions. I would offer though that the program is designed for you to create a separate credit card account with it's own individual transactions, each with it's own category, memo etc. The payment to the credit card account would be entered as a single transfer transaction from your bank account of choice. This method recreates 'real world' transactions.
I am not really worried about downloading from my banks and credit cards
If you decide otherwise, Moneydance uses direct-connect for online banking. This limits it's ability to mostly US-based firms. Here is a link to those supported firms. http://infinitekind.com/fi
Reconciliation and generating general reports is also available.