We haven't seen anything like evidence that our laws of physics are only approximations at all. If we're in a simulation, this implies that with high probability either a) the laws of physics in the parent universe are not our own laws of physics (in which case the entire idea of ancestor simulations fails) or b) they are engaging in an extremely detailed simulation.

It depends on what you consider a simulation. Game of Life-like cell automaton simulations are interesting in terms of having a small number of initial rules and being mathematically consistent. However, using them for large-scale project (for example, a whole planet populated with intelligent beings) would be really expensive in terms of computer power required. If the hypothetical simulators' resources are in any way limited then for purely economic reasons the majority of emulations would be of the other kind - the ones where stuff is approximated and all kinds of shortcuts are taken.

And our simulating entities would be able to tell that someone was doing a deliberate experiment how?

Very easily - because a scientist doing an experiment talks about doing it. If the simulated beings are trying to run LHC, one can emulate the beams, the detectors, the whole accelerator down to atoms - or one can generate a collision event profile for a given detector, stick a tracing program on the scientist that waits for the moment when the scientist says "Ah... here is our data coming up" and then display the distribution on the screen in front of the scientist. The second method is quite a few orders of magnitude cheaper in terms of computer power required, and the scientist in question sees the same picture in both cases.