Are there contemporary debates regarding this topic still?
To judge from the SEP article on mereology, the infinite divisibility of matter is indeed a topic of contemporary debate. See especially section 3.4 here: http://plato.stanford.edu/entries/mereology.
Do you think it's plausible that matter can be divided infinitely?
I'd distinguish between (1) the claim that every bit of matter is composed of smaller bits of matter and (2) the claim that, as a matter of physical law, those smaller bits of matter can always be pulled apart. (1) is a logically weaker claim than (2), so (1) can be plausible even if (2) isn't. I myself find (1) to be plausible. I take no stand on (2).
When we hear of experiments in modern physics where particles are collided and break into smaller pieces, does this constitute a division of matter?
Yes. Or at least I can't see why it wouldn't.