I'm the founder of Buxfer (https://www.buxfer.com)

Forecasting is one of the strongest aspects of our product. We also provide alerts ahead of time if we can predict your account balance will fall below zero (or whatever threshold you configure). Forecasting can also be used to preview your expenses/income/cashflow for the upcoming months / years.

We do have an API, but I admit it's not the best around. Other than that, our product does all the 6 things you point out.

Happy to hear more feedback at shashank@buxfer.com