You cannot add processing to clips in Cubase. You should give each clip its own track, or apply offline processing one fx after another. Each track can accept only 6 prefader plugins. There is no fx chains in Cubase. Export is SLOW, I bet it is the slowest among all DAWs, so if your recording is long, you will wait forever with export. Cubase is a bit overkill for such simple task as editing clips, and possibly not best suited for it. And it is quite expensive. It is a tool for music production, synths and arranging and notation, so with it you will be buying many functions that you do not need for your task.
IMO much better option for your work is Reaper. It has clip processing, meaning you can apply multiple fx to clips on the same track, in realtime. Export is great with Reaper, you can easily export clips as separate files. It works easily on extremely long recordings, I can import a month of radio recordings at once, onto one track, and edit it into thousands of clips, and has no problem with it. Also Reaper has the fastest export of all DAWS. And above all it is much cheaper, you can even try it for free.