No more discoveries for 2 years?

Not really as all data from the run 2 that just finished has not been analyzed yet. There will be no more new recorded data, but a lot of work is planned to exploit as best as possible what we have so far (LHC analyses take easily months, or sometimes even years, before being finalized).

I was watching a numberphile vid yesterday about Zeno's paradox, and at a certain point in the vid (10:53 min) he said that it would be interesting to ask a physicist if you can divide time and space infinitely, and a caption indicated that they will soon ask a physicist, but as far as I can tell they didn't.

I would say that at some point, when one approaches the Planck time/length, funny effects could occur. But this is just some naive guess :)