Questions about ability checks and multiclassing with spells.

[molean]

learned spells must be of a level you have spell slots for .... when you gain a level in this class, you can choose one of the <insert class> spells you know and replace it with another spell from the <insert class>spell list, which also must be of a level for which you have spell slots.-PHB for all sorts of spell caster classes

So let's say you are a Arcane trickster 9th lvl and 11 level bard. The multi-class guide says you would be a 14th level spell caster with 7th level spell slot. Does that mean said arcane trickster can learn and use 7th level wizard spells if that was the last class to get levels in?

Does Arcane trickster use spells like a sorcerer, interchangeably without preparing?

If the Arcane trickster multiclasses to wizard, can they copy and learn new wizard spells for their book and use them for Arcane trickster casting? And if so, to what level? Let's just say level 1 of wizard.

I've found multiple sources online that say bards Jack of all trades ability helps with Counterpell, even further stacking with Rogue's Reliable talent for guaranteed counters up to 8 even using 3rd slot. But I've been staring at Counterspells description for awhile and I'm not entirely sure how this works. I get most of the base principle but then doesn't this help with all spells? Like spells are resisted against the spell ability level + spell level, right? So are all spells boosted by Jack of all trades and Reliable Talent? If not, why not? How is Counterspell different than other spells? And what other spells are helped in this?

Does knowledge arcana not help with pulling off a counter spell? Yes I know it helps identify the spell being cast, but I mean the actual countering it.