I'm only going to speak on my expertise here which is Ancient China. I encourage others to ring in on this.

One can't understate enough how important supply lines and food was to winning battles.

1. Kind of a vague question so lets start from the beginning. A general wants to march to another city to attack. He first needs to calculate how many days it will take to arrive. Then he needs to decide either how long it will take for him to win the battle or how long he wants to continue fighting before retreating. He more than likely already knows how many bundles of grain feeds how ever many troops (I have no idea how much a bundle of grain was or how many troops it fed) so he will know how many bundles he needs. These calculations were more likely carried out by a supply officer or military adviser rather than a commanding general however.

Most food was put on carts pushed by horses. During the Three Kingdoms period, the Kingdom of Shu which controlled Southwest China had difficulty with supply lines due to the mountainous territory that they lived in, so Shu strategist/general Zhuge Liang invented a wheel barrow which was called the Wooden Ox. It revolutionized how grain was transported and made it much easier to transport supplies across the narrow and dangerous paths of the mountains.

2/3) Mainly grains such as rice, but they would occasionally have meat. It was also popular to bring wine as the drink.

4. I can't speak to the organization much, but supply officers were deemed in charge of supplies. So they were responsible for transportation, the storage depots and making sure the supply was not raided. Most famously during the Battle of Guandu during the pre-Three Kingdom's area, the warlord Yuan Shao charged his general Chunyu Qiong with the task of supply officer. Chunyu was left in charge of the supply depot at Wuchao, however Chunyu was only interested in drinking. Yuan Shao's enemy, the warlord Cao Cao (who was low on food), learned of the location of the supply depot and took advantage of the drunken Chunyu by conducting a night raid and taking Wu Chao. This swung the battle to Yuan Shao's eventual defeat.

5. This I have no idea to be honest.

6. See my first point.

Very broad question, what do you mean by ancient? Which army? Which war? These details will affect the answer given, but for the sake of example, I will give you what I can.

Here's the answers, for a Carolingian/Early French army:

1. A combination of bringing supplies, and eating everything they find.

2. Grain of all sorts. Rye bread, barley for gruel, etc. Anything that kept well was brought, so beets and other root vegetables are on the list. Meat will have to be from catching any animals while foraging.

3. Bringing animals is more difficult, so pulling grain carts, and soldiers carrying some on themselves is more common, but this isn't standardized.

4. Depends.

5. Yes, cooking would be necessary for some of the foodstuffs.

6. Stockpiling of surplus harvest, which is something that is always done in case of war or famine. When calling for a Bishop to bring his troops, Charlemagne specified that adequate supplies for a number of months must be brought as well.

Source: Excerpts from A History of Medieval Europe