I have setup the connections but I can't get the tasks to work. It's running now but there are 0 cotnacts brought over.
All the runs for this package are canceled, thus, we cannot tell you whether there were any errors or not, etc.
Also, as we can see you have created a Synchronization package. Note, that this package is used to synchronize data in both directions - from source to target and vice versa. If you need to migrate data from Salesforce to NetSuite one-way, you should use the Import package.
Some other issues we have are missing custom fields inside Netsuite we need data brought into
In order to see custom fields, you should select the "Use Custom Fields" in your NetSuite connection. This checkbox is used when you need to work with custom fields of predefined NetSuite tables in Skyvia. However, please note that processing custom fields may take a substantial amount of time, and it's better not to select this checkbox if you don't need to work with custom fields in Skyvia.
Please refer to https://skyvia.com/resources/docs/netsuite_connections.htm
Also, pay attention to the "NetSuite-Specific Features and Limitations" section.
Also we would like the ability to associate the contacts with companies inside NetSuite using a linked ID field inside Salesforce.
NetSuite Contacts table has the company_internalId field that refers to Customer, Vendor, Partner or Job object: https://www.netsuite.com/help/helpcenter/en_US/srbrowser/Browser2016_1/schema/record/contact.html
If you already have created companies (i.e. vendors or customers) in NetSuite, you can use Constant or Lookup mapping for this case.
Meanwhile, could you please specify this case in more detail, for example, specify what fields are used for Company Id in your NetSuite and Salesforce Contacts objects, whether these fields are custom, etc.?