Does the I-Mac have a built-in DVD MAKER

If you are talking about a DVD which can be played on and ordinary DVD player and watched on your television, Apple no longer supplies the software to create this. (iDVD was the app for this but it is no longer available.) There are third-party programs which can do this, 'Toast' among them, though probably none of them has the elegance of iDVD or its flexibility with menus. iDVD might still be available from independent retailers or eBay, but I don't know whether it will run on El Capitan. There is a forum for iDVD so that would be the place to ask about availability and compatibility.

No. However, I have just got a new iMac and was able to install iDVD from a previous Mac and it appears to work. I have not tried to burn a DVD using a connected optical drive yet.

I had not checked in a while. I have iDVD v7.1.2 that came installed on my 2010 iMac as part of OX10.6 Snow Leopard. I'd not used it in a while since a number of OS upgrades so just launched it. It appears to work normally with macOS 10.12.6 Sierra.

Mac OS no longer includes what's necessary - the new iMovie versions let you compose, edit, and put together a video, but it is geared towards sharing online, etc. It will not produce anything that can be played on a DVD.

As mentioned, in order to create a DVD which can be played on any DVD player, you need both software and a dvd burner. If you have the burner, but not iDVD (the discontinued Apple burning software), you'll need something like either Burn (free, but extremely basic) or Roxio Toast (not free, but the best around) or you can do a search for Mac DVD authoring or burn software app.

If you don't have a built in Superdrive, you can get a USB external burner.

Go to Apple menu > About this Mac > System Report > Hardware and look for Disc Burning. If it is there, you have a built-in disc burner.

Yes, I have the same on my 2010 iMac. But the OP may have a newer iMac without a built-in Superdrive.