In network terms, you can only send messages or wait for messages (or both), where message is quite literally a the digital form of a note at a piece of paper. There are size limits to the paper, but let's not go there now.
What you describe as "async request" is not a single message.
For example "user adding competitors". It needs an exchange of messages to know who you are ("user"), you need to get a list of competitors, and you need to send a subset of that list back. So it's not one request, it's at least 2-3 messages that fly across the network.
To get a better understanding, I propose that you play a game of network. Find 4 players, and find 4 pieces of paper, write "me", "server", "one friend", "second friend" at the top, and put them at separate places in your house or room. The piece of paper represents the knowledge of the person in the game. Each player also gets a load of small notes, and a pen to write the messages.
The rule is that each player may only use information he knows by himself, or information from the piece of paper. (This is the hard part of the game, you are easily tempted to use more information than you have according to the rules).
Everybody can send a message, a short line of text of a few words (say, less than 8), a question or a statement. The server can send to anyone else, all others can only send to the server.
You send a message by writing a note, folding it, bringing it to the other person, and leaving without a word (going back to your paper).
When you get a message from someone, you may read the note, copy any information from the note to the paper, and then discard the note.
You may also modify or delete the information on your own paper as you like.
Now try to do 1 and 2 in that game. You'll be surprised how many notes you need to exchange (especially the server) to get agreement.
In the same way, you can also try different ideas in what you call "sync request".
At a more serious level, the thing you are trying to understand is called "protocol". A protocol is a set of messages that have a properly defined (and agreed) meaning. For example, if I say "Hello", you know that I mean to greet you, rather than I expect you to pay me a thousand dollar. We both know the message "hello" and we both agree on its meaning.
There are lots of protocols, and there also exist protocols for chess playing, eg
https://chessprogramming.wikispaces.com/Protocols?responseToken=e7442a33e8385089777b3984be5a04ea I am sure there are many more, just search the Internet a little.