If you are connecting, you have few worries. In the unlikely event of a misconnect, you will be rebooked. Similarly, if this is a connection, it means that there is an interline agreement and ANA will check your bags through to TPE.
As to the other situation above, it is all about risk tolerance because he is not connecting as he is on separate tickets. If there is a significant delay on the inbound and the passenger no shows for his onward flight, depending on that onward ticket's fare rules, he may be required to purchase a new ticket at walk up prices. I am uncomfortable with short transfers unless the onward ticket can be replaced cheaply and the risk of getting stuck for an appreciable period of time is minimal.