If I send some bitcoins to some address, and I pay the proper fees, how sure am I that it will be included in the next block? Are there any guarantees if I want my payment to be included in the next block that is mined?
Actually just pay recommend fees you can get your transaction sent less than 10minutes. Guaranteed
Your transaction will be relayed across the network in seconds for sure, but nope you can't be sure that it will be confirmed within 10 minutes.
As time between blocks is random, it is not uncommon to see no new blocks for half an hour or more.
what i meant is, is it also not sure that your transaction will not make it to the next block? can the next block be full of transactions and you will be waiting for it for the block after it?
Correct.
Right now bitcoin block has a maximum size of 1 MB. As I said sometimes there is no block for a long period of time, then there will be a huge number of unconfirmed transactions queuing and you will see a couple of "almost full" blocks afterwards.
But in most of the times, your transaction will be confirmed in the next block as long as you pay the standard fee.