Two confirmations is better than one because to reverse the tx an attacker would need to make a longer chain and the more confirmations that a tx has the further back the miner would need to go to produce the longest chain which doesn't include the tx. If a tx has 2 confirmations to be reverses an attacker would need to produce 3 blocks before all the good miners combined make 1. If the attacker only makes 1 or 2 he is still behind. 60 blocks is better than 2 because for an attacker to attempt to reverse this would require making 61 blocks before all good miners combined can make 1. This is essentially impossible unless an attacker has 51% or more of the global hashing power.
I think somehow despite two dozen explanations you don't understand what a confirmation means.
Say the most recent block is 10009.
(unconfirmed tx)
Block 10009
Block 10008
Block 10007
Block 10006
....
Block 1
Block 0 (genesis block)
If your tx is not in the blockchain it is unconfirmed (0-confirms). If your tx is in block 10009 (the most recent) then it has 1 confirmation. If your tx is in block 10008 it has 2 confirmation. etc.
What happens if two miners generate a valid block a the same time? Which one wins?
Neither each will broadcast their block to their peers and those peers will build off that block. Temporarily the network will be split some miners building off block "a", some building off block "b". Eventually one side will solve the next block and the other chain will be orphaned.
Example:
current block is 1000
Miner A produces block 1001a, Miner B produces block 1001b. Part of the network believes block 1001a is the correct block, part of it believes 1001b is the correct block.
Eventually someone will produce block 1002. If block 1002 builds off block 1001a then 1001b will be orphaned and all miners will build off block 1002 to produce 1003, 1004, etc.