Was there a pre-determined arrangement for the division of Germany in case it surrendered before any Soviet forces entered its territory?

Q Was there a pre-determined arrangment for division of Germany in case it surrendered before any Soviet forces entered its territory?

Yes. The allied had many plans for that. But many were not as recognisable as the later boundaries that evolved into state borders. Example from Churchill's ideas at Yalta:

More on the outline of a history of either partition or outright dismemberment plans: Philip E. Mosely: "Dismemberment of Germany: The Allied Negotiations from Yalta to Potsdam", Foreign Affairs, Vol. 28, No. 3 (Apr., 1950), pp. 487-498.

Q … so I thought that maybe, from this standpoint, it would have been better to concentrate resistance on the eastern border and let Western forces invade deeper.

That is exactly what many generals advocated for and what after Hitler's death the new "Flensburg Government" ordered its soldiers to do.

Dönitz's initial priority was to open communication with the commanders of German armies, and to establish with them their acknowledgement of his new authority as sole Supreme Commander of all German armed forces. He also sought their agreement with his overall policy of negotiating successive partial surrenders with the Western Allies, while maintaining the war against Soviet forces in the east.

The very result of this policy in German tactics was thus:

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Q Was there any predetermined arrangement, official or non-official, to divide its territory into sectors in the case of Western powers occupying the whole of the country before the Soviets managed to enter it?

The arrangements that came after February 1945 in Yalta and were drawn up in the minutiae of the European Advisory Commission, and then largely finalised in Potsdam mainly spoke of given the Soviets a share in zones. But these were in flux for quite a while.

Montgomery's 21st Army Group (later) advanced to the Rhine with operations Veritable and Grenade in February 1945. A meticulously planned Rhine crossing occurred on 24 March. While successful, it was two weeks after the Americans had unexpectedly (sans meticulous planning) captured the (railway) Ludendorff Bridge at Remagen and crossed the river on 7 March. Montgomery's river crossing was followed by the encirclement of German Army Group B in the Ruhr. Initially Montgomery's role was to guard the flank of the American advance. This was altered to forestall any chance of a Red Army advance into Denmark, and the 21st Army Group occupied Hamburg and Rostock and sealed off the Danish peninsula. On 4 May 1945, on Lüneburg Heath, Montgomery accepted the surrender of German forces in north-west Germany, Denmark and the Netherlands.

With small alterations the occupation zones had some slightly bigger, some slightly smaller changes, not only at Potsdam, even long after the German capitulation. Example:

On 13 November 1945 Barber and the Soviet major-general Nikolay Grigoryevich Lyashchenko (Russian: Николай Григорьевич Лященко) signed the Barber Lyashchenko Agreement ((in German), also Gadebusch Agreement) in Gadebusch, redeploying some municipalities along the northern border between the Soviet and British zone of Allied-occupied Germany. Thus some eastern suburbs of Ratzeburg, such as Ziethen in Lauenburg, Mechow, Bäk and Römnitz became part of the Duchy of Lauenburg District (British zone), while the Lauenburgian municipalities of Dechow, Groß and Klein Thurow (now component parts of Roggendorf) as well as Lassahn (now a component part of Zarrentin am Schaalsee) were ceded to the adjacent Mecklenburgian district (Soviet zone). The redeployment was accomplished on 26 November, the respective occupational forces had to withdraw until 28 November to their new zonal territory.

Q Would the Soviet sector have covered less ground than it did in actual history? Or it would have been the same, and there was no benefit from letting Western forces advance deeper?

Leaving out the hypotheticals: the fiercer resistance towards the Eastern forces did enable more Wehrmacht soldiers and civilians flee to presumably more favourable British and American forces and territory. This also was one factor that did enable the British to prevent Soviet boots on the ground from reaching the North Sea. Obviously a possibility the Western allies had in mind, whether because of imprecisions in agreements, angst to find a fait accompli or beginning mistrust in Soviet policies is irrelevant.

Nevertheless, concentrating all resistance towards the East would probably not change the fact that the Soviets would have gotten "their share". One reason being that when really more concrete and realistic plans for the division were drawn down, the Soviets had already crossed the border and made facts. These were the realities the Germans feared the most. Concerning any allie dplans for divisions, the most 'popularised' plan that the Germans were aware of was the Morgenthau Plan from 1944. It wasn't a very favourabe prospect for directing military resistance either.

As an unconditional surrender was agreed upon as the ultimate goal quite early on, any German aspirations were moot in the end. But why should they have set their eyes on any of these plans as the most realistic or probable one and arrange their military tactics towards –– which one?

A history of partition plans with pictures:

Cover of a 1945 Dutch book about the annexation of German territory (NIOD)

Sumner Welles’ proposed partition of Germany, published in Life magazine, July 24, 1944

Franklin Delano Roosevelt’s proposal for occupation zones in Germany, drawn in pencil by the president himself while en route to the Cairo Conference of 1943. From Earl F. Ziemke, The US Army in the Occupation of Germany 1944-1946 (1975)

Map of a possible partition of Germany published in Time magazine, February 21, 1944 (Robert M. Chapin Jr.)

Map of the division of Germany from the Yalta Conference in February 1945 (Library of Congress)

It may be of interest that quite a few hardened German soldiers and anticommunists were speculating on being recognised as the "defenders of Western Europe" (from bolshevism) - and that indeed some Western allied plans went equally into that direction: eliminate Hitler, but then march on Eastward towards Moscow, with newly (re-)formed German batallions: Operation Unthinkable. As everyone was a lot of spitballing at the time, from German fantasies, Churchill's ideas or British plannings, not much of this met the approval of the Americans, as far as they became aware of any of this.

The requirement of unconditional surrender was decided by the Western Allies in January 1943 in Casablanca. Even earlier all Allies promised not to conclude a separate peace.

There was no arrangement and no accepted plan of what to do with Germany before the beginning of 1944. In the early 1944, when it became clear that Germany will be defeated soon, there was a discussion what to do with Germany when it is defeated. Various plans were discussed by the Allies. See, for example the Morgenthau Plan.

According to Wikipedia,

The Morgenthau Plan was seized upon by the Nazi German government, and used as part of propaganda efforts in the final months of the war which aimed to convince Germans to fight on.