Once blockers are declared, that's set in stone. Even casting a removal spell on a blocker doesn't cause the attacking creature to become unblocked.

So yes, casting a pump spell after declaring blocks is perfectly fine here.

Yes. As stated in the Oracle rulings for Leyline of the Void, "Tokens can still die while Leyline of the Void is on the battlefield." They aren't cards, so the Leyline's replacement effect will never apply.

First question: Yes, copies of spells are still spells.

Second question: On the stack and during resolution, there's little difference between them. They're spells but they aren't cards, they'll exist on the stack, resolve, then cease to exist. If a permanent spell gets copied somehow, the copy will resolve and create a token with its statistics.

The most relevant difference between the two is that your "passive" copies aren't cast. This means that they won't trigger any "whenever you cast..." abilities (this is why the magecraft abilities in Strixhaven trigger "whenever you cast or copy..."). It also means that certain spells might behave differently when they're copies.

Things like a value of or whether a kicker cost was paid are copiable attributes that are kept when the spell is copied, but, for example, if you flash back Increasing Savagery (to get 10 +1/+1 counters) and then copy it, the copy will only add 5 +1/+1 counters because it was not "cast from a graveyard" (or for that matter anywhere else).

That's correct. No name is not a blank name, it is no name. Objects that have no name can't "have the same name" as anything.

It will be legendary.

With the original wording of Sakashima the Impostor, there would be a decent argument that it's nonlegendary, as the 'still' in the text would mean the copy effect isn't changing its legendary status.

Unfortunately for you but fortunately for everyone's sanity, the card has gotten an Oracle text revision: You may have Sakashima the Impostor enter as a copy of any creature on the battlefield, except its name is Sakashima the Impostor, it’s legendary in addition to its other types, and it has “: Return this creature to its owner’s hand at the beginning of the next end step.”

When you cast Sakashima, The Sixth Doctor will trigger and copy it. The copy of the spell will be nonlegendary, but when Sakashima the copy enters the battlefield, its copy ability will make it legendary again.

You can get around this to a degree, however, because like most clones, Sakashima's ability is a may. You may choose not to have the copy enter as a copy of anything, in which case it will be a 3/1 Creature - Human Rogue named Sakashima the Impostor. It won't have any abilities, but it also won't be legendary, so it's better than nothing.

Yes.

When you pay 1 life and exile a blue card to Force of Will, you aren't bypassing the cost, you're paying an alternative cost. The new cost to cast the spell is "pay 1 life and exile a blue card from your hand." Tax Collector's effect will add a mana to that total cost you pay.

The difference between this effect and Trinisphere is that Trinisphere will add whatever amount of mana increase that brings the cost up to 3. It will increase the cost to cast Force of Will to 1 life, exiling a blue card, and paying because the casting cost being paid didn't have any mana. On the other hand, if Force of Will were cast for its mana cost, Trinisphere would do nothing since it already costs at least , but Tax Collector would still increase the cost from to .

Tax Collector also isn't symmetrical, while Trinisphere is, so in the second case you'd have to pay to cast that Opt.