first some comments on stuff already posted.
btw, it looks like we start on a hill/grassland, which is actually a nice tile because you get some food from it as well as shields.
have i been playing a different game? city tile still produces same thing as in civ3, 2 food, 1 hammer and (i dont remember if it makes money).
In some cases, chopping produces more then 30 hammers, I think 51.
i'm fairly certain that the 51 is on games of different speed. fast games i think are 51 (though i dont remember the number, using yours), normal are 30 and epic are 20 something (21 iirc)
Some improvements on top of a forest (like building a mine) include the forest chop in the total time to complete, but I think you get the bonus hammers in the middle of the total time, as if you had chosen to just cut down the forest.
i've had them come in at completion of the mine i was building (on a forested hill), so i think you're wrong there about the timing. and i have yet to find a worker action that builds on a tile (thereby removing the forest) that does NOT give a city the bonus hammers.
Settling on floodplains gives you a -3 health. They give you extra food, though.
you sure that its the place you settle? i thought it was number of floodplains in city radius as StanNP posted 3 posts above yours.
I won't touch the hills; I hope for them to grow forests.
having not yet had a forest grow (i improve all tiles i can) why would you want this? i mine hills as soon as i can. what effect does a forested hill give that i dont know about?
now for my own observations.
i see 4 silks on the map. (where warrior is, SE and E of warrior, and N of settler)
for the first turn, i'll move the warrior NE so that i can see if there's anything good on the tile SE of that. If it is a good one, then i'll move settler 1 east and settle, this adds the 3 unseen tiles to the east to the city (hopefully something good in there, i think one of em is a hill) even though it does make me lose the silks that the warrior is standing on, but one of 4 aint a big loss for the gamble on 3 additional tiles.
if the tile the warrior reveals (N+NW of settler) is a bad one (like plains or grassland with no bonuses) then i'll move the settler one South and settle. This leaves the city with a all the river squares it has now (ie settling without moving) and leaves it all 4 Silks and the gems and corn ofcourse. and i'm fairly certain this spot (1T S of settler) is still on the river, so still getting the health boost. but the important part to me is that it will add 4 unseen tiles to the city radius. with the rate of bonuses i've seen in my games so far, i think there's a good cahnce atleast one of the 4 has a bonus.
because forested tiles do not get the river +1coin bonus, and all 4 silks are on the river, and all 4 are in forests, i think one of the first tasks i'll have a worker do is chop down those forests and improve the silk tiles with whatever fits them best (farms or mines, if mines are possible, dont remember).
with the river bonus coin and the silk bonus coin, those tiles will be making 2 coins each. 2 of them are grassland under the forest, so that will be 3 food and 2 gold with farms. and 2 are on plains, so thats 2 food 1 hammer and 2 gold with farms. and with the huge gold bonus from the mined gems my research will go like as if i had a library up.
i like letting my cities grow to size 2 before i start the first worker, and i can usualy get a warrior out of the city by then to explore with more then just the one warrior i start with.
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maybe you could post a zoomed out screenie with that because now I'm really confused as to the locations of the resourses (SW looks like a grass/forest to me, not a resource 
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The starting moves will propably be moving warrior to the hill and if he doesn't see anything good settle in place. From my very limited experience i would say that going for an early religion is not a good idea unless you start with mysticism (which seems to be civ4 version of alphabet 
