Hi,

I would like to be able to integrate Doit.im with the project management platform I use for my business.

There is also the lack of a Linux app (I use a Mac on the go and Linux Mint at home) which would be less of a problem with an API available.

I think the best and the easiest to implement (on both sides) is a RESTful API.
Here's an example of a (almost) perfect API implementation:
https://www.dropbox.com/developers/core/api

I know that in the past there was an API (although I never had the opportunity of using it). Whatever happened with it?

Thanks,
Marius