1. Is it possible to play by giving orders to complete platoons,
Yes, and the game is pushing strongly to it, making it difficult to micromanagement.
or must you control individual tanks, squads or heavy weapons?
You can control individual squads, but not must.
If yuo can give orders to platoons, are your platoons pre-organised for you,
Yes platoons pre-organised as in real life, but you can change this.
or do you have to group them (as in Theatre of War)?
As I recall TOW not have platoons and even squads functionality have appeared only in the latest versions of game.
3. Is it possible to organise a typical offensive operation - advance to contact, assault, and re-organisation - by a company-sized force, or a platoon sized force, in formation?
What do you mean by the re-organization? In tactical battle or in operation?
Formations not have any limits, you can make it from any quantity of units.
You can send in formation a battalion or even regiment if you have it on tactical battle.
Say, I am a tank company commander, with three platoons with no attached infantry. I want to form up with a tank platoon leading on the left, another tank platoon leading on the right, company HQ (me) behind them in the middle, and behind company HQ, the third tank platoon - in other words, I want to advance 'two up' ('inverted wedge'). Or the same, if it's a '3 rifle platoon+coy HQ' infantry company. (or if the scale is smaller, ditto but with tanks or infantry squads in formation).
In the game it looks a little different - the formation of units = group of units united by a shared work process (path) and "target".
Game not support strange constructions like wedge or V on unit basis. But you can do this on squad/platoon/coy basis due to right order sequences with time delays.
Can you organise it so the platoons don't just start in this formation, but maintain it ('taking their dressing', say, from the front left-hand platoon) and work through a typical attack and re-organisation?
This will not happen automatically. Game does not support the inviolability of platoon's "borders" or mutual bind one to another.
For example, let's say I want my tank company to cross the Start Line in 'two up' formation and advance to the objective in this formation. I want the left tank platoon to assault the left-hand part of my objective and the right platoon, to assault the right-hand area. While they are doing this, I want company HQ (representing me) to stay just behind with the third, 'depth' tank platoon staying behind me/Coy HQ, ready for me to order in, as my reserve, as and where needed.
You can send it manually like any other game or use time management mechanism for group tasks. No scripts programming or somthing like this in this game.
3. Is there some form of realistic radio traffic? If one of my platoons hits contact, will they report it on the radio - where it is and what it is, at least? Will they call in sighting reports? Or tell me on the radio, if they hit an obstacle or for any reason, become unable to follow the orders they have been given?
Radio is very rare visitor while in the army. But if you have for example modern DLC from 80s or tanks with radios, you have a radio traffic and ability to automatic fire control if its possible. In WWII times most communications through voice, signals or wire phones - and yes this modelled in game too.
You can see where I'm coming from - what I want in a tank/infantry RTS (actually = real time TACTICS, not strategy) game is for it to simulate not wargaming with miniatures, but war. No criticism intended, for anyone who is happy with the 'wargame with miniatures' approach.
Yes we try to do this.