Not jquery, but you definitely don't need it for this. If you really wanted to then change to querySelector or whatever it is in Part 1.

Part 1:

document.getElementsByTagName('P');

Part 2:

const config = {
    childList: true, // Includes text nodes that are added or removed as children of the target element.
    subtree: true  // Also monitors changes to all the target nodes descendants.
};
let observer = new MutationObserver(function(mutations){
    mutations.forEach(function(mutation){
        processMutation(mutation)
    });
});
observer.observe(document, config);

processMutation(mutation){
    if(mutation.type == 'childList'){
        for (let i = 0; i < mutation.addedNodes.length; i++) {
            doStuffWithNewP(mutation.addedNodes[i], 'added');
        }
        for (let j = 0; j < mutation.removedNodes.length; j++) {
            doStuffWithNewP(mutation.removedNodes[j], 'removed');
        }
    }
}

doStuffWithNewP(node, state){
    // do stuff
}