Disguise Self / Silent Image when camouflaging an item into another item

Question

A spellcaster uses Disguise Self to pass as a simple bodyguard. In particular, the quarterstaff that she uses as a spell focus, which normally looks like an obviously magical item (runes, faint lights, the works), is disguised to look like a simple martial weapon (the kind of quarterstaff that a monk would use).

She is asked to drop her weapons in a box before meeting a mob boss. She doesn't want to reveal that she is a spellcaster.

1. At the moment where you cast the spell, Disguise Self applies to belongings on your person. What about afterwards? Would the quarterstaff, once put in the box, immediately take back its previous appearance?

2. If the answer is "yes", could Silent Image be used to maintain the illusion? I would want to create the exact image of the fake quarterstaff "around" the actual quarterstaff to keep it camouflaged. Is that a possible use of the spell? Would someone picking up the quarterstaff, without examining it too closely, immediately notice the illusion, assuming the weight/material of the illusion is similar to the real one?

3. Is it still possible to control the illusion (in particular, to keep it around the quarterstaff if it moves) even after the spellcaster has dropped her spell focus?

Answer 1

You can try

TL;DR — as a player, you can try and see what happens, but only your DM knows for sure.

Everyone plays D&D a bit differently, sometimes more than a bit. Aside from rules as written, only the DM knows how magic works in their world, so you have you ask this particular DM.

There is no game text that explain all the corner cases. It's the DM's job to adjudicate them:

A spell's text details the spell's effects—the only thing the spell does. Any additional effects are up to the DM.

This was explicitly clarified in the Tasha's Cauldron of Everything source book:

The DM Adjudicates the Rules

the rules can't cover everything. When you encounter something that the rules don't cover or if you're unsure how to interpret a rule, the DM decides how to proceed

So what are the DM's options? The Disguise Self spell's text states:

You make yourself — including your clothing, armor, weapons, and other belongings on your person — look different

The easiest option is probably say that "on your person" is the requirement of the spell. So the moment the caster drops an item it takes its original look (the illusion is dismissed).

Would someone picking up the quarterstaff, without examining it too closely, immediately notice the illusion, assuming the weight/material of the illusion is similar to the real one?

Yes, since any physical interaction reveals the illusion per RAW:

The changes wrought by this spell fail to hold up to physical inspection.

could Silent Image be used to maintain the illusion? I would want to create the exact image of the fake quarterstaff "around" the actual quarterstaff to keep it camouflaged.

Probably yes, but the spellcasting process itself is noticeable, so it won't work right in front of the guard.

Is that a possible use of the spell?

I'm sorry, but it's the thing only your DM knows. Ask your DM.