1) Turn 1 - Axis player attacks 1 hex for free, then after that both players must roll initiative to determine who attacks first in the next attack?
On turn 1 only the Axis player makes any attacks. The Axis players makes as many or as few attacks has he chooses and when finished you move on to the movement phases.
After turn 1 there is a roll to determine who makes the first attack. The second player then gets to make an attack and players alternate until both no longer wish or can attack.
2) Attacking - After the 1st round of combat (attacker goes, and then defender's remaining units). Does combat continue if the attacker still has units and so desires?
I'm not quite sure what you are asking here. But each attack is only one round. A hex may be attacked more than once but each attack from any one hex has only one round. Forget any other A&A games you have played when playing BOTB. The combat system is not similar.
3) Combat Phase - After being attacked. Does the defending player have the option to withdraw all surviving forces (those with 1 hit [forced to retreat] and not hit)?
The only forces that move during the combat phase are those that are forced to retreat. Surviving units in a hex may move during movement.
4) Combat Phase - Retreat. If defending player has truck with him and it survives can that truck take the supplies in the hex and retreat 1 hex back (along with other survivors)?
A truck may move during movement and take the supplies with it without using a supply token. A truck may move troops and supplies if a supply token is paid to activate the hex for movement. This refers to trucks in enemy ZOC and that have not been commandered by the other side. Trucks not in enemy ZOC automatically return to the off board area.
5) Truck and Supply Losses - a re-clarification. Say that I have 3 infantry and 5 supply tokens. The attacking player rolls 4,4,4. The infantry does not get hit, but the supplies get hit. Question, do I lose only 3 supply tokens?
That is correct. I often, at least as Allies but supplies and trucks in a hex as "fodder." I don't so often as Axis as they have fewer supplies and trucks