I am very new to Salesforce and I need to write a trigger which should fire on few formula field updates and should update the other fields in contacts and accounts. So something like this:

Trigger should fire when updates are done to these fields:
From Contact object fields - ED_180_Prior__c (formula date field), Prof_Status__c (text)
From Account object fields - M_Status__c (formula text field), Days_of_MT__c (formula number field).

Trigger should update these fields:
From Contact object - Pardot_ED_180_Prior__c (date field), Pardot_Prof_Status__c (text).
From Accounts object - Pardot_M_status__c (text field), Pardot_Days_of_MT__c (number field)

I have tried this so far:

    trigger updatePardot on Contact (after insert)
    {
        List<contact> conUpdate = new List<Contact>();
        set<Id> sAccId = new set<Id>();
        for(Contact con: trigger.new) {
                sAccId.add(con.AccountId);
        }
        List<Account> lstAccount = [select id, Address_1__c, (select id,Address_1__c from contacts) from account where id IN: sAccId];
        for(Account acc: lstAccount) {
                for(Contact con: acc.contacts) {
                       //con.Address_1__c = acc.Address_1__c;
                       con.Pardot_ED_180_Prior__c = con.ED_180_Prior__c;
                       con.Pardot_Prof_Status__c = con.Prof_Status__c;
                       conUpdate.upsert(con);

                       acc.Pardot_M_status__c = acc.M_status__c;
                       acc.Pardot_Days_of_MT__c = acc.Days_of_MT__c;
                       lstAccount.upsert(acc);
           }
       }
   }

Can someone please help me if I am not doing it correct, or if I should change the approach as soon as possible? Also, should I setup workflow rules for every different field when this trigger should fire? Much thanks in advance.