When resolving the modes you have chosen for this ARTS's ability, you resolve them in the order they are written. You may not resolve the modes in any other order.
For example, if your opponent has Code Love Heart CMR on the field when you use this ARTS, and you select the modes "Return 1 of your opponent's SIGNI to their hand." and "Draw two cards." as this ARTS's effect, you may target your opponent's CMR and return her to your opponent's hand. Then, since CMR is no longer on the field, CMR's [Constant] ability is no longer active. You may then resolve the "Draw two cards" mode of this ARTS's effect.
However, if you select a SIGNI other than your opponent's CMR, you will not be able to add cards to your hand, as CMR's [Constant] ability will prevent you from adding cards to your hand.
This ARTS's "Your opponent's LRIG cannot attack this turn" mode changes a game rule, and does not affect your opponent's LRIG.
This ARTS's effect will bypass the protection of No Gain, as No Gain will only protect against ARTS abilities which will affect LRIGs or SIGNI, but not be able to protect against a change in the game rule.