@mrbarletta was misinformed back in 2021

SalesAgility never removed the YUI library in version 7.11.6 of SuiteCRM
YUI v2 is available on every page of SuiteCRM current version 7.14.6

As for your question:

popups are opened in SuiteCRM with the global function open_popup
which has this signature (apologies for missing type information)

function open_popup(module_name, width, height, initial_filter, close_popup, hide_clear_button, popup_request_data, popup_mode, create, metadata)

This will open a popup search window
You can also open your very own custom windows with this function

SUGAR.util.openWindow

signature (no type information):
SUGAR.util.openWindow(URL, windowName, windowFeatures);

As for ajax
SuiteCRM uses jQuery for this
I would recommend you look at https://api.jquery.com/jQuery.ajax/