office 365 vs Appication that latest updates

we are in the process of moving to office 365 and come a cross major issue is that some  applications are not supporting latest IE and the windows updates . how we can go on this without any disturbance to the current operation . our office 365 people are recommending to have the latest in both the case ( updates and IE)  to get the full version from the office and mail client end  . coz we have E1 E 3 and Mail P1 .

another party is saying we can go with the  Both = latest - 2  ? which one is the right one for me to  trust and some are saying office 365 migration is not a issue . issue is the application compatibility and the future release support level of our internal application match that level  .

we have more than 20  plus applications covering VB6 to .net to web base application running on the company . is there anyway to check the application compatibility via tool or we need to check one by one . please help on the information and the experience on this