No you do not because the ones that you will used for the tribute is your opponent's monsters.
Soul Exchange targets so you've already chosen which monster you'll be allowed to use, before you activate Psi-Impulse. You can't just decide to tribute a different one. Soul Exchange never forces you to actually use the monster, you're not obliged to use it at first opportunity. Even if you did target an opponent's Psychic monster for Soul Exchange, you are not forced to use it for Psi-Impulse if you'd rather use your own.
Soul Exchange lists no such requirement. If you wanted to tribute summon, you don't need a monster on your side of the field for their monster to 'take the place of', you are simply using their monster to pay the tribute cost.
Yes. Soul Exchange requires you to use it as a Tribute at the first opportunity.
No, it requires a Tribute. Unless stated otherwise, like on cards such as Soul Exchange, a tribute must be something you control. You cannot tribute an opponent's monster as a cost for your own effects or summons.
It does target, it targets the monster you want to tribute. After Soul Exchange resolves, that one monster now has a lingering effect applied, that lets you use it as a tribute instead of tributing one of your own monsters.
Clearing up some possible confusion - Soul Exchange doesn't 'take' monsters, nor does it do anything to them on resolution, except for set up a condition that says you can tribute it as if it was one of your own. You tribute it therefore in exactly the same way as if it were on your side of the field. There is nothing stopping you tributing it, and a monster on your side of the field, to summon a Lv7 or higher monster. In fact if you used 2 Soul Exchanges, you could summon a Lv7+ monster with both of them.
No part of The Wicked Eraser's effect stops you from tributing it with Soul Exchange, or stealing control of it with Change of Heart and tributing it after.
No, you do not 'tribute' the Synchro Material for a Synchro Summon. They are sent to the graveyard, not tributed. You can tribute an opponents synchro monster for "Assault Mode Activate!" to summon the assault mode monster from your deck.
A Tribute must be a monster you control, unless specifically stated on the card. Cards like Soul Exchange, and Chimeratech Fortress Dragon, specifically let you use an opponent's monster. But Malicious Edge does not say so, so normal tribute rules apply.
You can only ever Tribute something that you control, unless specifically instructed to do otherwise. Cards like Lava Golem and Soul Exchange for example, are cards that specifically say the opponent's monster can be tributed.
Soul RopeTRAP/NormalActivate only by paying 1000 Life Points when a monster you control is destroyed and sent to the Graveyard. Special Summon 1 Level 4 monster from your Deck.Soul Rope is activated when a monster is destroyed and sent to the Graveyard. This means that you can activate it when a monster you control is destroyed by battle or by another card effect. You cannot activate Soul Rope if the monster was destroyed during the Damage Step via a card effect such as a Defense Position Berserk Gorilla because the timing would not be correct. You also cannot activate this card if there is an effect that prevents your monster from being sent to the Graveyard (ie. D.D. Warrior or Macro Cosmos).
Yes you can but you have to tribute one of your monsters, as well as the one of your opponent's monsters that you tributed using Soul Exchange.