[SalesForce] How to enable permissions on the partner object for the api user

Sure, you can use the Metadata API. You want the create() call. Here's the sample xml to define the custom object from the documentation:

<?xml version="1.0" encoding="UTF-8"?>
<CustomObject xmlns="http://soap.sforce.com/2006/04/metadata">
    <deploymentStatus>Deployed</deploymentStatus>
    <description>just a test object with one field for eclipse ide testing</description>
    <fields>
        <fullName>Comments__c</fullName>
        <description>add your comments about this object here</description>
        <inlineHelpText>This field contains comments made about this object</inlineHelpText>
        <label>Comments</label>
        <length>32000</length>
        <type>LongTextArea</type>
        <visibleLines>30</visibleLines>
    </fields>
    <label>MyFirstObject</label>
    <nameField>
        <label>MyFirstObject Name</label>
        <type>Text</type>
    </nameField>
    <pluralLabel>MyFirstObjects</pluralLabel>
    <sharingModel>ReadWrite</sharingModel>
</CustomObject>

Actually, the PermissionSet SObject has a field in it called IsOwnedByProfile. Take a look at this blog post by Adam Torman, http://blogs.developerforce.com/engineering/2012/06/using-soql-to-determine-your-users-permissions-2.html:

This field determines whether a permission set is a custom one or if it is parented by a profile. This is made possible because for every profile, there is one underlying permission set. That way, permissions layer equally across permission sets without having to treat a profile differently.

So, if you want to find the CRUD permissions of a profile you can do something like this:

SELECT Id, SObjectType, PermissionsRead, PermissionsCreate
FROM ObjectPermissions
WHERE parentid in (select id from permissionset where
PermissionSet.Profile.Name = 'System Administrator')