How to make wp plugin auto-refreshing on the public side of view (auto load page) - ajax

Question

First have to say that almost every time when searching on technical solutions.. search engine will direct me to this site here. I admit that i have learned such A LOT here just by searching through for answers..
but also have to say that not being a coder.. so don't understand much here at all ;)
Ok, the Problem:
Want to update wordpress tables or calendar within wp admin. These changes should become updated on the public side automatically and more or less instantly (~ few seconds is perfectly fine).
I found solutions about manipulating header.php, i found some ajax plugins I found -too much to count- info on how to implement ajax into wp
Sadly.. none of these could help me through as the plugins mostly either not work, are outdated or require countless file edits. Manipulating header.php seems odd.. as i don't want to loop-refresh the whole page, post etc.. but only get e.g. table or calendar data updated.
So maybe any of you coders know of something to e.g. get the plugin "All-in-One Event Calendar by Timely" to update the public visible part of the calendar once data edited in wp admin?
Greatly appreciate pointers in any direction to solve this.
P.S.: What would you think of plugins like "ajaxify everything" ? don't know if this really the way to go..
Again, thanks for your help, time and contribution!!
update
additional question:
I now found such plugin to let me chose which parts i want to "ajaxify".
Such plugin would ask me for a specific function name.
Now, where do i start to gather this information?
Below is the instruction from the plugin context inside wordpress admin
Generate Ajaxized DIV for your function
Ajaxize will allow you to ajaxize almost any php function on your
site.
It can be a plugin, a function you wrote, or even a core wordpress
function.
There are some (obvious or less obvious) limitations currently:
Functions must return valid HTML - this will be called in php and returned via the
Ajax call
Functions cannot accept any parameters (at least at the moment)
Enter a function name below.
Function Name: xxx input field xxx what put in here? xxx
The generated div can be inserted to any page/post on the site and
will ajaxize the call to the function automatically.
Please make sure you enter a valid function name, that the function
does not require any parameters, and that it returns valid HTML.

Answer 1

In your context you want to refresh the calendar automaticaly when there is a change in the WP_Admin;
but you can't exactly do this.
You can write a Js method which will check the time of lastest modification of the calendar at the load of the page, stock it in Var.
After you'll have a constant (each 10seconds) Js "daemon" which will get the time of lastest modification of the calendar and compare it to the stocked Var; If change you reload the calendar.
PS: Ajaxify everything is not really a solution due of the developpement you need To Ajaxify and to code for people who has disabled Javascript.
Hope it helps