I do not want to disclose my actual product idea, so the questions below are built for a similar popularity product.

I want to launch a product to the market that is for the Instant Pot Pressure Cooker: Instant Pot - America’s #1 pressure cooker, multicooker
The product is a cooking tray that goes into the instant pot.

Here are my questions:
1. When naming my product, can I legally play off the Instant Pot name? Examples: InstantTray, Instant TrayPot, Instant PotTray?

2. In my product descriptions and titles online, can I use the trade marked name in phrases such as "Great for the for the Instant Pot", or "perfect addition to the instant pot", or "cooking tray for Instant Pot"?

3. Can I legally get the parts to build the tray from a few different manufacturers and piece a kit together that I sell as my own? Do I have to disclose all the companies in which I got all the parts from when advertising and marketing?

4. I don't want instant pot, or anyone else to build a tray like this. I've never filed for a patent, but do I have any leverage in claiming that my product is specifically for the pressure cookers therefore preventing others from advertising and marketing for it?