It's not super clear to me what you are actually wanting to do.
Your other slotted characters may not be doing anything because 1. they may not have a target selected, or 2. they do not have any in game skill bound to the key combination you are sending to the game instance.
Currently you have two menus.
Standard menu
New Menu Key menu
You set the buttons on the Standard menu to target the character in Slot 3 of your character set. This means that if you click on the green boxes, or press the Hotkeys assigned to the menu (the 1 to = keys), then the appropriate menu button will send 1 to = to ONLY the character in Slot 3.
For the New Menu Key menu, you have set the target to the character in Slot 2 of your character set. You have also set this menu to be the ALT+1 to ALT+=, for both the Hotkey set and the resulting actions on the buttons. In other words, if you click on the green boxes for this menu, or press the ALT+1 to ALT+= hotkeys, then they will send the corresponding ALT+1 to ALT+= to ONLY the character in Slot 2. The ALT as referenced in the picture here is the ALT key on your keyboard, not alternate character.
They way you appear to be trying to set it up is so you have a bunch of individual bars, which you can click on, or press Hotkeys for, that will trigger skills individually on different characters. This is a pretty inefficient style of multiboxing, but it is multiboxing, and a little more advanced that ALT+TAB.
If you want a click interface, rather than a Hotkey driven interface. Don't set hotkeys on your menus. Your biggest issue will be if you want to use Hotkeys to trigger skills, then with an individualised setup as you are doing, you will run out of keys on the keyboard very quickly.
If you want to have separate menus that send the same key to the individual characters, then set the buttons in each button set to do so. It seems odd that for your New Menu Key menu you are not just sending the standard buttons 1 to = in the button set. In your setup this is skipping the default skill bar that is normally configured in most MMO's. It is allowable to have button sets that send the same Key Combination to different game instances.
Finally, if you keep going down this particular route, your will run out of screen space for all the menus you will have. In a general MMO, you can have 4 hotbars, or 48 buttons. If you create menus to control each one individually you would need 12 menu bars for your 3 characters. EQ has some other system of it's own, which IIRC will allow upto 150 or so functions, so you could get very crowded.
If your problem is because your other characters do not have a target selected, then usually you have them perform an Assist prior to sending the actions on the buttons.
There are two methods to this.
1. press ALT+A first, then click the button
2. have the button execute the Assist Me mapped key first. You can see an example of this in the Standard Assist+Broadcast button set.
Of course, this will only work if you have configured an /assist social as
described here.