Hello,
1) Backtests and studies on our website work with EOD data only and they simulate trading decisions at the market close time. So they use Close prices to open/close positions at the exchange close time. You can imagine it like you check prices just before market close and immediately make decision (or use MoC orders).
We also tried the approach you described (check Close price, make decision at next open), but we moved away from that, because in many cases the Open price is already way too far and the signal is no longer valid.
2) The PTL Trader application will work intra-day (so it will evaluate signals and open/close positions during the whole day), but you can restrict open/close trading time windows, so you could say something like "only evaluate signals and open new positions at the end of day", if you wish.