Here is some useful order of battle information:
http://www.orbat.com/site/ww2/drleo/000_...000oob.htm
http://www.bayonetstrength.150m.com/
http://web.telia.com/~u18313395/normandy/index.html
http://www.winterwar.com/Numbers.htm
http://dspace.dial.pipex.com/town/avenue/vy75/toe.htm
http://www.wwiidaybyday.com/ had lots of original German org documents but it appears to be down at the moment, maybe try again later?
Anyway, to briefly address a few of your points:
Halftracks were generally issued only to the infantry, engineer, and reconnaissance elements of armoured units. The proportion so equipped depended on doctrine, organization, and most of all availability. The Soviets never developed their own tracked infantry carrier and so relied on the relatively small numbers of lend-lease machines they received, mostly for recce outfits. The vast majority of Red Army "mechanized infantry" simply rode on the tanks and dismounted when brought under effective fire.
The British infantry bn included a carrier platoon of 13 Bren Carriers, this seems like a lot but they could only carry 3-4 men plus an MG/ATR/mortar, so they did not materially improve the mobility of the battalion as a whole. They were mostly employed for scouting, as a mobile tactical reserve, and for supply distribution/casualty evacuation over ground covered by enemy fire. The lend-lease US halftracks were concentrated in the motor battalions of armoured brigades to allow the infantry to accompany and intimately support the tanks in action.
Americans used halftracks in much the same way, equipping the armoured infantry battalions of armoured divisions. Regular infantry made do with trucks or their feet. It really doesn't make much sense to spread them around as a unit moves at the speed of it's slowest member, if everyone isn't mounted that means walking pace, which is a waste of the vehicle's inherent mobility.
Germans wanted to equip all of their panzergrenadiers with halftracks but production never came close to meeting this goal. Most panzer divisions had one PzG battalion out of four so equipped. Certain elite/high prestige units such as Panzer Lehr in Normandy had more than this.
Yes, there was proportionally a lot more infantry back then. Armies were larger and industrial bases smaller, plus the amount of ground that needed to be covered was vast.
By "tanks in support" I presume you mean in direct cooperation with regular infantry units? Not the tank-infantry team within an armoured division? If so, yes, most of the Allied nations continued to devote tanks to infantry close support throughout the whole war. They had such an abundance of materiel that such profligacy was possible. The Germans knew they could never match their enemies in production and so elected to almost totally denude the regular infantry of armoured support in order to concentrate what assets that did exist in the panzer divisions. They argued, and I think most historians will state with some justification, that a hundred tanks attacking on a front of two kilometers is more likely to achieve a decisive success than three hundred attacking over a frontage of fifty. The results of the early campaigns bear out this idea. Some concessions to armoured support for the regular infantry were made, most notably being the StuGs. These were usually in independent corps-level battalions handed out to infantry divisions as a reinforcement for important operations, in the same way supporting artillery would be allocated. From 1942 a small number of self-propelled antitank guns [Marder series, StuG III and IV, etc] came in to use in German infantry divisions also to counter the massive numbers of Soviet tanks. Usually no more than a single company in the divisional antitank battalion, the bulk of antitank defense still fell upon towed guns right up to the end of the war.
Most nations did not generally mix heavier and lighter tanks in the same tactical [battalion level] organization. They were seen as a higher reserve breakthrough/counterattack force to be saved for "special occasions". Thus, you have your Red Army Independent Guards Breakthrough Tank Regiments with KV's and later JS-2's, etc. For a brief period when first introduced, the Germans fielded the Tiger in mixed battalions incorporating Panzer III's with short 75mm guns for scouting and close support, but this was soon dropped. They went to all-Tiger units with three companies of 14 vehicles each [3 platoons of 4 plus another 2 in the headquarters].
The Panther, while heavy by other nations standards, was not classed as a heavy tank by the Germans. It was intended to equip one of the two battalions in the divisional panzer regiments, the other Bn being Panzer IV's or in some cases StuGs due to production shortfalls. Again, the Germans tried to avoid mixing multiple vehicle types in the same Bn, this simplified maintenance and ammo supply.
Tank destroyers...again, depends on nation and doctrine. Every US division had a tank destroyer Bn, whether armoured or infantry. Germans had some in their divisions, but still relied mostly on towed PaK. British the same. Soviets generally kept them as part of the tank/mechanized corps, but like everything else, had independent Stavka Reserve formations that could be doled out to anyone based on need. I don't know if the Stavka reserve formations were subordinated to the local unit once deployed, or if they remained under control of higher headquarters. Knowing how the Russians like to do things, probably the latter.