lurker's comment: With techs, I would be pondering between Sailing > Optics and Mining > Masonry. Both Writing and Animal Husbandry I would consider less interesting options just now.
Mining itself only lets you chop the dyes forest, there's not much else for the worker to do without having more advanced techs first, so switching production to a boat does indeed look interesting. Setting the capital to gold focus would let the to be born citizen drop on the dyes tile, then the trireme would indeed be built in 8 turns (3x5 + 5x6). That means no production decay on the worker yet, because that only happens after 10 turns with units (50 turns with buildings).
Where your units are they're only preventing barb camps to be spawned, as they're eliminating the fog. I wouldn't mind a barb camp, actually, to give them something to do.
You're unlucky with this mountain ridge. This isn't how the game is meant to put you. The Continents map only has a very limited amount of mountains. Maps with more mountains, like Pangaea, Archipelago and Small Continents all include a rule that eliminates mountains on the coastline, by turning them into hills. The continents map doesn't have this rule, but it has very few mountains, so the chance of a start position like this occurring is very slim.