Adding Custom activities and Activity logs using rest api.

Hello,

We are in process of integrating marketo with our platform and here is a use case that we not able to solve using rest api.

1. We have some custom activities we want track which are not available  on marketo. Like for example creating a project or an organization. I know there is an Rest API endpoint for adding custom activities, but it requires a activityTypeId. Where can i find that?   

2. Now every time a lead perform any of these custom activities we want to insert a record in the leads activity log using REST API (because we can only verify in the backend that activity is performed, Button Click wont work for us). I could not find an endpoint for this.  Is it possible to perform this action using a REST api endpoint? if Yes can you please point me to the page? if no is there a reason this is not available or is it not recommend to insert activity log records using an API call.

Any help is highly appreciated.

Thanks