Hi Asser,
1. You are quite correct. Once the historical data has been loaded into EA Studio, everything else happens locally on your PC. No internet connection is required.
2. On MT4, once an EA opens a trade, based on the real-time price, the TP and SL are ‘saved’ with the broker, so if your internet connection goes down, or you have a power failure, the trade will stay open until the SL or TP are reached, however the indicator rules will not apply, and of course, no other trades will open or close. Remember, the EAs reside on your PC, not your broker’s server.
Hope this clears things up.
Ilan