How does Counterspell work and can it be used on Silence?

Can Silence be Counterspelled?

Silence: For the duration, no sound can be created within or pass through a 20-foot-radius sphere centered on a point you choose within range. Any creature or object entirely inside the sphere is immune to thunder damage, and creatures are deafened while entirely inside it. Casting a spell that includes a verbal component is impossible there.

Counterspell: You attempt to interrupt a creature in the process of casting a spell. If the creature is casting a spell of 3rd level or lower, its spell fails and has no effect. If it is casting a spell of 4th level or higher, make an ability check using your spellcasting ability. The DC equals 10 + the spell’s level. On a success, the creature’s spell fails and has no effect.

Let’s take a few specific scenarios before you just tell me Yes of course.

Issue 1: First off the NPC would have to know a Silence is being cast. How would they know this until its too late?

Issue 2: Would it depend on position and environment? Say my character is on the other side of the room and there’s melee going on. Likely to not hear. Vs standing next to the NPC Caster and its quiet. I guess in that case they could potentially understand what spell I’m doing?

Issue 3: Would having Silence themselves play a role? What I mean here is I could see if a Wizard NPC has Silence and Counterspell ready then perhaps they recognize Silence as I cast it. If they don’t know Silence though then how would they know what random draconic I’m uttering?

Some of this may be broader mechanics of Counterspell – namely should the DM know what’s being cast before deciding to Counterspell and how would they? And specifically how, if at all, could it be used on Silence?

Backstory for anyone that may care: DM was telling us all week to be ready for an epic fight because we hadn’t had one in a while. She rolled low on initiative and I rolled well enough. I cast Silence and she did not counterspell it. She was then all bummed because we killed the Wizard before he could get a single hit off (our Fighter crit him and Paladin knocked him prone). She blames herself for not using Counterspell. The more I think about it though the more I don’t know how she should even be able to have used Counterspell.