Ugh......a seemingly easy enough question, with a not so easy answer. Well, here goes....
First off, For the sake of discussion purposes, I don't want to get bogged down in the semantics of what constitutes a Panzer IV F2. There are many highly acclaimed books which make a formal distinction here.....and those that say such nomenclature is no longer valid. Jentz states on page 8 of Osprey's Panzerkampfwagen IV, Ausf G, H and J that: "There is no difference between a Pz.Kpfw. IV Ausf F2 and a Pz.Kpfw. IV Ausf G - they were simply different names for the same model of Pz.Kpfw. IV".
"The F2 is basically an early G, so to speak. The F2 only existed from March 1942 until July 1942 when all F2's were renamed G's, from then on it was known as a G model. There really is no difference between an F2 and a G, since they are the same tank. The thing is, that there were modifications made during the production run.
The muzzle brakes are NOT how you tell the difference, since the G models had the single chamber muzzle brake until September 1942, when it was replaced by the double chamber muzzle brake. Likewise, the L/43 and L/48 guns are NOT how you tell the difference either, since the G model did not get the L/48 gun until April 1943.
Best way to look at it, is that the F2 and early G's are the same (since the F2 was renamed G anyways), then you have a line of G's with several modifications added, then in May of 1943, the H model comes out.
The Osprey New Vanguard #39, Panzerkampfwagen IV Ausf. G, H and J, by Tom Jentz and Hilary Doyle, has an excellent explanation of everything, and it is a recent publication, so it is not full of all the old myths, legends and misinformation."
Let's just say we are talking about the first batch of Panzer IVs that featured the long-barreled, 75mm, Kw.K. 40 L/43 gun with the "globular-type" muzzle brake and still retaining the turret vision ports. Is this definitive enough?
Secondly: We know that Totenkopf spent the winter of 1941 encircled in the Demjansk Pocket. It did not breakout until April of 1942. It remained at the front, but was held in reserve until Oct. 1942, when it was withdrawn to France for rest and refit. Most sources state that Totenkopf received it's Panzer Regiment at this time, (Oct-Nov, 1942), however, page 215 of Panzer Truppen, Vol I, states that two light and one medium Panzer companies were created for Totenkopf on June 1st, 1942. Since Totenkopf was not returned for refit until Oct. of 1942, I'm not quite sure how it could have received it's Panzer Regiment any earlier than this date. A division decimated to 20% of it's original strength from months of hard fighting would have little time for training on it's newly formed Panzer Regiment while still engaged in combat at the front.
The Panzer IV "F2" was produced between March-July of 1942. If Totenkopf didn't receive it's Panzer Regiment until Oct-Nov of 1942, one would think all of the "F2s" would have been issued to other units by this date. I don't seem to be able to find any photos of Totenkopf "F2s" either.
Since there has been a considerable amount of mix-up in nomenclature in many books...(is it an Ausf F2 or is it an early G), one can not be certain which variant a particular author is referring to in any given book, since not all authors make the distinction in the name change and date. All we are left with is interpreting the photos.
If anyone wants to add to this mess, feel free......
As for divisional symbols on Tiger II and Panthers....By the time these beasts made their debut on the battlefield, the use of divisional symbols had greatly waned. Sure, you can find examples of vehicles still decked-out with a full complement of markings at this time, but as the war dragged on, use of divisional markings fell away. Generally speaking, they would be found on the upper right hand corner of the glacis plate, (as you would face the vehicle) and sometimes the opposite rear corner as well. It is best to consult photos of particular vehicles to determine whether or not they carried these markings at the time.