Edit
As of the latest Steam / Civilization versions, this problem has been fixed. Launching the game regularly from Steam opens only the Civilization-specific selection window, and right-clicking that menu and creating a specific DirectX-11 link will create a shortcut that shows no DirectX-selection menus.
Original answer:
I'm not sure the "why" is really on-topic here, I just think someone made a mistake. I share your pain.
As for a solution - I've searched online and experimented a bit, and while I could easily bypass the first dialog, I could not bypass the second. To bypass the first dialog, just don't click "play" directly in the Steam game library. Instead, choose one of the following:
- Run the Civilization V exes directly, found in your installation folder, which should be in
<steam folder>\steamapps\common\sid meier's civilization v. It doesn't matter which one you start, unfortunately, they all open that 2nd dialog.
- A more convenient way for the above method is to ask civ to create a desktop link. In the 2nd dialog, right click and choose "create dx11 desktop shortcut". Keep in mind that despite the name, it will prompt the 2nd dialog.
- Use Steam's "jump list" to launch the game. Just right-click the steam icon on the taskbar and choose "Civilization V" from the list:
This issue is also being actively discussed on the Steam forums, with no resolution at the moment.
Notice there's a difference between improving a tile and working a tile. Usually you will improve tiles around your cities and then send citizens to work these tiles, but this connection is not necessary.
Improving a tile
To improve a tile, you need it to be within your cultural borders (the tinted area) and reachable by a worker/work boat, and you need to have the appropriate technology. Once a tile is improved by the worker, you get any luxury or strategic resource on it, but that doesn't mean you get the tile benefits (e.g. +production, the small hammers) - you have to work a tile for that.
Pay attention: cultural borders can reach practically everywhere, since cities can expand these borders up to 5 tiles and great artists can expand it arbitrarily further. I once used 3 great artists to reach a far away tile (Aluminum...), it takes time because there's a cooldown between cultural bombs, but it's doable. "Culture bomb" is the name of the great artist's ability which does it. However, in practical terms, if you want access to any resource the best way is to build a city up to 3 tiles from it. Usually when I build a new city I only consider things in radius 3 to be interesting, anything beyond it just usually takes a lot of turns to get.
Notice that some worker actions, such as cutting down a forest or building a road, do not require the tile to be within your cultural borders.
Finally, if you build a city directly on a tile it doesn't count as improving the tile (the tile benefits won't change) but you do get whatever resource is on it.
And as Raven mentioned, to improve tiles at sea you must construct a work boat from a coastal city. Unlike workers, work boats are consumed when they construct an improvement, but they are otherwise very cheap.
Working a tile
To work a tile, you need it to be within 3 tiles of one of your cities, and then that city gets the benefits listed on the tile. In your screenshot, Krakatoa is unworkable, and no civilization will never get the benefits listed on the tile. Notice that even tiles in range 3 are not automatically worked, a citizen must be allocated to it. You can manually allocate citizens from the city screen but the computer takes care of it by itself, if you're new to the game you don't need to worry about it at this stage.
Your puppet cities also send their citizens to work nearby tiles, but you cannot change that allocation.
A tile doesn't need to be improved in order to work it, but most tiles benefit from improvement so ultimately it pays to improve any tile within range 3 of a city. Improving a tile beyond range 3 which doesn't have a resource on it offers no benefits (unless you improve it to a fort or something).
Best Answer
If you want the best possible relationship:
It is nearly impossible to do that if you're already mid-way through a game. The way that your 'reputation' works with other AIs is that if they can't do anything and you're in their way - They'll start to hate you. Even if you're their military supplier or the 'guy' who gave them (other nations) all the gold you earn etc.
There is no way to make AI players voluntarily want to ally with you, unless you do something that they like (ie. Go to war with someone they're at war with).
The way relationships with other states work is that you have to share a common goal with them in order to get 'on their good side'; be allies/friends.
Other than that - It's nearly impossible to get world peace (everyone allied with each other).
For some problems such as building wonders that they want to build (and already having built them), there's nothing you can do; nothing can be demolished (except for tile upgrades).
Example: I was a warmonger (had heaps of military units), but didn't use them to attack other nations. However, all the other nations except for one hate (and constantly denounce) me as they themselves were warmongers and was at war with another nation for constantly denouncing them.
There was no way I could improve my relationship. I've been accepting all their demands, gifted them everything, agreed to their wants in the world congress and everything for over 400 turns. Every time I improved my reputation with them (they start to like me), it went down again (they hated me more).
EDIT: The only way I could make them start 'liking' me was to destroy my huge army, which would leave me vulnerable to their attacks as they had a descent army themselves (around 10 units, compared to my 50+ units)