Thanks for asking.
To create custom post types, please take at following article:
For latter part of your question it will require some custom development which falls outside the scope of support we can offer. However, I can point you in right direction to help you get started. I suggest you to setup child theme for the same. You can take a look at following resource to get started.
Next, you can copy
x/framework/views/global/_index.php to child theme in the same order. After that you need to add the necessary PHP code to check for different category archives pages and display the corresponding The Grid shortcode. Same will require use of conditional tags. To help you get stated with the same I am sharing relevant resource, please take a look.
To get started with The Grid plugin, please take a look at following resources:
In case you are not comfortable with programming, you should get some professional help by getting in touch with a developer.
Thanks for understanding.