I assume you mean Ritual Summon, as Relinquished can't be summoned by tribute summon.
Once Relinquished is on the field, you as the turn player have Priority, you can start a chain by targeting an opponent's monster with its Ignition Effect. The opponent is free to chain to this as normal. If it resolves properly, Relinquished will be equipped. You can ask to enter the battle phase, but remember the opponent doesn't have to let the phase pass if he's got something he wants to use, so he can use something to possibly destroy Relinquished first.
So basically, you can certainly summon Relinquished, and on its first turn (not THE first turn, of course, no attacks can be declared) , steal a monster and attack, but not 'immediately' in the sense that the opponent gets chance to respond to every part of the process.
I assume you mean 'Ritual Summon'. 'Immediately' is a poor term to use in Yu-Gi-Oh as it implies some kind of rush to do something before it is no longer allowed - everything has a correct 'timing' but they rarely conflict. I will outline a valid turn that uses Relinquished, to show what it can do. In Main Phase 1, the turn player plays Black Illusion Ritual. If it is not negated, Relinquished is placed on the field. Now the summon can be responded to, Relinquished can use his absorption effect here. The opponent can chain to this, but if the effect is not negated or the target lost, then the target will be equipped to Relinquished. Destroying Relinquished in response will not save the target, it will end up in the graveyard anyway, even though Relinquished has already left the field. The turn player can then declare he wishes to proceed to the battle phase. If the opponent has nothing he wants to activate, then the battle phase is entered. Relinquished can now declare an attack, which can be responded to as normal.
A Level 8 monster needs two tributes, so you can tribute a Lv5 monster, but must also tribute a second monster too.
A level 7 monster needs two tributes, so you can tribute a level 6 monster but must also tribute a second monster.
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.
It is a Lv6 Normal Monster so can be Tribute Summoned by offering one monster as tribute.
I assume you mean 'Ritual Summon'. 'Immediately' is a poor term to use in Yu-Gi-Oh as it implies some kind of rush to do something before it is no longer allowed - everything has a correct 'timing' but they rarely conflict. I will outline a valid turn that uses Relinquished, to show what it can do. In Main Phase 1, the turn player plays Black Illusion Ritual. If it is not negated, Relinquished is placed on the field. Now the summon can be responded to, Relinquished can use his absorption effect here. The opponent can chain to this, but if the effect is not negated or the target lost, then the target will be equipped to Relinquished. Destroying Relinquished in response will not save the target, it will end up in the graveyard anyway, even though Relinquished has already left the field. The turn player can then declare he wishes to proceed to the battle phase. If the opponent has nothing he wants to activate, then the battle phase is entered. Relinquished can now declare an attack, which can be responded to as normal.
Relinquished is Ritual Summoned with the Ritual Spell Card Black Illusion Ritual. It requires a monster as a Tribute to Special Summon Relinquished from your Hand. Once Relinquished is successfully Ritual Summoned, if it is sent to the Graveyard, it is eligible to be Special Summoned from it. You cannot Special Summon Relinquished from the Graveyard unless it was successfully Ritual Summoned first.
No, that's not possible. The tribute summoned monster is placed on the field immediately after the tribute is offered. Nothing can go in between these, let alone a Spell Speed 1 spell card.
You can tribute a special summoned monster, yes.
A level 7 monster needs two tributes; you can tribute a level 5 monster but must also tribute a second monster.
A level 8 monster needs two tributes, so you can tribute a level 6 monster but must also tribute a second monster.
A Level 8 monster needs two tributes, so you can tribute a Lv5 monster, but must also tribute a second monster too.
A level 7 monster needs two tributes, so you can tribute a level 6 monster but must also tribute a second monster.
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.
It is a Lv6 Normal Monster so can be Tribute Summoned by offering one monster as tribute.
You can tribute a monster when an effect instructs you to, or you need to do so as a cost. So you can tribute a monster for a tribute summon only in your own main phases, when there is no chain in progress. You can however tribute a monster for one of Enemy Controller's effects at Spell Speed 2, in either player's turn, in any phase.
Yes, you can tribute an XYZ monster to tribute summon something.