I've created a tile overview in my SiteCollection that links to pages within subpages. When I chose to insert webparts I don't see webparts from the parent page. Is there a way to use those tiles as an overview in the subpage as well?
When you develop a web part, you can Export it and then Import it so it becomes available when you go to the Add Web Part menu.
With your page in Edit Mode, click the little arrow in the top-right corner of your web part and click Export. You'll download a file that'll contain your web part's contents.
Now navigate to your destination page (the page you'd like the web part to be on) and enter Edit mode. Go to the Add Web Part menu like normal, but look in the bottom left corner for the "Upload a Web Part" link. Use the browse and upload buttons to upload the file you downloaded during the Export process.
Your custom web part should now be listed under the category Imported Web Parts.
For more info and screenshots: Exporting and Importing web parts in SharePoint 2013