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I am playing an Investigator Interrogator in a free-archetype Pathfinder 2e campaign (we get archetype feats at every other level, starting from level 2).
Which Intelligence-based free archetype (preferably with spontaneous spellcasting since that is more flexible, but prepared is OK too) would give me access to most of these detective-like spells I have found so far: Object-Reading, Locate, Ring of Truth, Discern Lies, Scouting Eye, Pinpoint, Proliferating Eyes, Detect Alignment, Impecable Flow?

I am new to Pathfinder, so I don’t have a grasp of which spellcasting archetypes get access to which spells, and the Archives of Nethys pages on these spells also don’t list which classes and archetypes have access to these spells.

Somewhat unrelated to the question above, I have also considered taking the Alchemist Archetype, just because it would allow me to craft the Silvertongue Mutagen and get a bonus to Diplomacy and Intimidation (but since that would be the only boost to my detective abilities the Alchemist archetype would grant me, it isn’t that enticing). How many free archetype levels would I need to sink into the Alchemist to be able to craft the Major Silvertongue Mutagen?

Pointed Question:
"You ask a question that charms or needles someone in just the right way. Ask a question of a non-allied creature that you can see. Attempt a Diplomacy check against the creature’s Will DC. The creature is then temporarily immune for 1 hour.

Critical Success The target must directly answer your question. It doesn't have to answer truthfully, but you gain a +4 circumstance bonus to your Perception DC if the creature attempts to Lie to you. Whether it answers truthfully or not, you glean something from its body language, and it is off-guard to the Strike you make using Devise a Stratagem against it before the end of your turn.

Success As critical success, but the circumstance bonus to your Perception DC is +2.

Failure The target can refuse to answer you as normal.

Critical Failure The target can refuse to answer you as normal, and its attitude toward you decreases by one step due to your aggravating attention."

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I am not entirely clear whether the creature becomes off-guard both on Critical Success and Success, or only on Critical Success.

I am also not clear whether the creature becomes off-guard only if you besides succeeding on the Diplomacy check also succeed on the Perception check to determine whether it is lying or not.
The rule says, "Whether it answers truthfully or not, you glean something from its body language...", but I am not sure whether that means that you get that bonus even if you fail in determining whether it is lying or not.