Do players start with any initial Warlight Coins or do they need to be purchased?
There will be some limited quantity of free coins, but there will not be much since coins are worth actual money, so if we gave out too much we’d go bankrupt.
Are there any other specifications other than 0% Luck, SR, Cyclic move order?
There can't be any randomness that affects one players differently than others. So cards must also be given out on a fixed schedule. Random warlords is okay since it happens before the game starts. Wastelands are okay as long as scenario distributions aren't used.
This could however be easily exploited with the use of second accounts.
Using multiple accounts for coin games (or sharing accounts) is strictly against the rules. Anyone caught would get their account banned and lose all their earnings. Given how big of a risk that would be, it's unlikely this will be a problem.