Meantime, do keep in mind that this is a peer to peer forum. Garmin employees sometimes read it and (very) infrequently post. If you really need action on a problem, a call to tech support is your best bet.
I feel your pain. I'm continually going to their website to manually delete tracks. When I share my location before heading out the old tracks just confuse the people I'm relying on to track/monitor me.
It's a minor issue but the repeated poke in the eye of doing it (or the complaints if I forget to) have rubbed me a little raw.
I find the site overall very confusing. Using it with "other" devices, adding devices, etc is impossible to navigate.
There is a relatively easy way to handle visibility of tracks on MapShare. On the Social tab of your account at explore.garmin.com, click the Filter MapShare Data button.
The most straightforward thing to do is to set the start date under the heading Hide Older MapShare Data. Typically, I set this at the start of each trip. That way, only data for this trip shows up.
If you are into the whole "collections" thing, you can also manage this with one collection per trip. After you create the new collection and link it up properly, you can use the section Make Collections Visible on MapShare to limit it to the collection for the current trip. This always seems a lot more complicated to me than setting the date. But it does work. If you do change collections frequently, you do need to remember to change these settings anyway.
Don't forget to click Save Changes at the bottom of the pop-up after you set the date or adjust the visible collections.
For personal accounts (which I assume is what you have), you can effectively have only one iR device per account. The site does torture you a bit making that apparent, but that's the bottom line.
"Other devices" is a bit odd. Not making excuses here - it really does require you to understand more than a little about the whole Garmin ecosystem. The ecosystem is made up of a bunch of what appear to be independent Garmin properties - explore.garmin.com, connect.garmin.com, mygarmin.garmin.com, etc. Some of these have related mobile applications like the Explore app, Garmin Connect mobile app, etc.
These properties are not really independent. They are all tied together by Garmin single signon. When you are signed into one of these properties (explore.garmin.com in our case), you are also signed into any of the others which you might visit (mygarmin.garmin.com in our example here). And in a lot of cases, creating an account at one of the Garmin properties will also create one on some of the other properties. This is supposed to make things simpler for you - and it does as long as you don't think too hard about what's happening under the hood. And as long as you only have ONE set of Garmin credentials (or, if you do have multiple accounts, you only sign into one at a time on a given browser platform).
Usually, there is more than one way to handle something like adding a device. I have two devices on my explore.garmin.com account - an iR device and an F5X+ watch. I honestly don't remember how I added the watch. Pretty sure I did it via the Garmin Connect mobile app and the Explore mobile app (probably with help from the Garmin Express desktop program - see below). Based on what I am seeing on the explore.garmin.com site (when I click Add Other Device), it looks like I could register a new device on the resulting mygarmin.garmin.com page and it would appear in my explore.garmin.com account.
Assuming, of course, that the device is compatible with the Explore site. Most new devices are compatible. Many older devices are not.
There are other odd warts that don't exactly fit the single signon model. Garmin Express is a desktop application that you use, among other things, to register devices and get firmware updates. Garmin Express does not require you to sign in. And it maintains information about "known" devices on the PC itself, not via online accounts. But there are places where it does interact with the whole signon ecosystem. For example, when you register a device, it will require an account under which to register it. Pretty sure it says this is a Garmin Connect account, but the information about the device spreads all over the ecosystem.
As I said, it doesn't pay to think too hard about this stuff.