I made a bitcoin address here:
How can I then send bitcoin from there once it receives some? I can't find any website services or android apps which let me import a private key to do that. (And to check the balance)
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Fortunately you have many options.
The bitcoin core client allows key import with
Adds a private key to your wallet. Requires a new wallet backup. Hint: use importmulti to import more than one private key.
Note: This call can take over an hour to complete if rescan is true, during that time, other rpc calls may report that the imported key exists but related transactions are still missing, leading to temporarily incorrect/bogus balances and unspent outputs until rescan completes.
Alternatively there are many wallets out there that allow importing or sweeping a private key. Some of these include Electrum, Mycelium and Samourai (these are examples, not recommendations).
Lastly, coinb.in, the site you used to create the key allows you to build a transaction and sign it as well https://coinb.in/#newTransaction. I wouldn't recommend this for a novice user as you can end up losing your funds to miners fees if you do not include a change address. If you don't know what a change address is don't attempt this approach. You can practice on testnet or with small amounts until you get comfortable you know what you are doing.