Sharepoint - How to provide contribute without edit permissions?

Create a custom permission level by copying the contribute permission level and remove Edit items option.

To create a permission level

• Open the site collection site (the root site not a subsite)
• Go to site setting.
• below Users and Permission > Click on Site Permission.
• From the above ribbon, > click on permission level to be able to create a new permission level.

For more details check

• How to create a new SharePoint permissions level
• Configure custom permissions in SharePoint 2013
• Understanding permission levels in SharePoint

Alternative solution using Item level permission

For more details check How to enable Item Level Permissions in SharePoint

You can create your own permission level same as contribute, but without edit option.

Below is the link for reference. https://technet.microsoft.com/en-us/library/cc263239.aspx

You can use that Standard available Contribute Permission profile

Your "View Own Items" restriction is a setting on the List, not in the Permission profile