Learn Croatian: Moj suparnik priprema samo zamke.

To say someone 'sets' or 'plants' a trap subversively, you use the verb podmetnuti (or imperfective podmetati). The phrase podmetnuti zamku perfectly captures the stealthy, underhanded nature of the prefix pod- that you are currently learning.

Is there a way to use the prefix nad- to talk about dealing with a suparnik (rival)?

Yes! If you want to say you outdid or surpassed your rival, you would use a verb with the nad- (superiority) prefix, such as nadmašiti (to surpass) or nadvladati (to overcome). For example: Nadmašio sam svog suparnika (I surpassed my rival).

Could I put samo at the very beginning of the sentence, like Samo moj suparnik...?

You could, but it changes the meaning. In the current sentence, samo (only) modifies the word after it, meaning he prepares only traps (and nothing else). If you put it at the beginning, it means only my rival prepares traps (and nobody else does).

Why does the word for 'traps' end in -e here?