All the info you seek is in the game rules.
https://365.strat-o-matic.com/help/rules/baseballIn the autodraft, if two players rank the same player #1 then a random decision is made on which of the two (or three or four if more people in the league rank him #1) - the loser of the random decision will get the next highest priced player that is not on another team's draft card at that players primary position.
Losers of random decisions are then MORE LIKELY to win the NEXT TIE (if any)
If two players pick the same player, then the one who ranks the player HIGHER on their draft list will get him.
In your last paragraph, you are correct on all of that.
For more detail, see the game rules.