As you can see here, the gold contens of a chest very much depends on the arena you currently participate in. You say it is Arena 3 (Barbarian Bowl), so that's what I am assuming throughout the reset of the answer. Higher arena means more gold, so faster gold-getting!
A silver chest will give you (averaged) 38 gold, and a gold chest 127 gold. I disregard the giant and magic chest, see that as a bonus if it pops up :). There are 180 silver and 54 gold chests throughout the whole cycle (source), so roughly 3 silver chests per 1 golden chest. If you open them in order (that is, SSSG), you'll be netted (38*3 + 127) = 241 gold in 17 hours (3*3 + 8).
However, there are also free chests and the crown chests, that add to this amount. You'll get roughly 4 free chests in this time period, and 2/3 of a crown chest. I'm not sure how much this is, feel free to comment this if you are on arena 3 and open a free/crown chest, I'll add it in. This depends on your playstyle: if you play only a few games per day, not enough to win the crown chests, it takes longer. If you play just once a day, you can only open 2 free chests, instead of the theoretical maximum of 6.
Furthermore, you can donate cards in your clan and get money (and experience) in return. How much you donate is completely up to you. As told here, it is a maximum of 4200 gold per week. You'll get 5 gold for a common donations and a staggering 50 gold for a rare donation.
In conclusion, it differs quite much per player. If I can get the gold per crown/free chest, I will calculate the approximated time when you play at maximum efficiency.
Unfortunately, there is no Global Chat. There have been discussions of such feature on the Supercell Forum, but the idea has been ruled out.
A possible reason for not having Global Chat might be to cut back on spam and inappropriate language, as Clash of Clans contains a fair amount. Although this causes some issues with recruitment, people can use the forums as recruiting center in place of a Global Chat.
Best Answer
In any competitive game there is something called "game sense", what this means is that as you play the game you start to understand the intricacies of the game and is able to do certain things that an inexperienced player wouldn't do.
As for Clash Royale, you need to understand what deck your opponent is playing and be able to understand how much elixir your opponent has based on the cards he has played. For example after your opponent goes all in with hog/goblins/prediction log, you need to be able to add the elixir of those cards, which happen to be 8, so after you defend this push and has units left over, you can get a huge counter push and your opponent will only have 3 elixir to defend.
Basically, there is no correct way to count elixir, pros can do this because they play a lot and are naturally good at keeping a clear mind. Just keep playing, and understand how to properly punish your opponent for making bad all in plays.