when you talk about "speed of bitcoin transactions" there are two things that you should not confuse with each other: the confirmation speed and propagation speed.
when you send a transaction it only takes seconds to propagate throughout the network. it is usually less than 10 seconds. in other words when you send a transaction, the other party receives it almost immediately.
but as you may know a transaction needs to be confirmed to be finalized and the receiver be sure about it. and confirmation means being included in a block and blocks are found every 10 minutes on average.
with that said, these days because of the large number of unconfirmed transactions in the mempool and the full blocks, there is a competition going on to get in the next block. and like any competition if you are ahead of others you will "win that space" faster than them. you can see how much you have to pay in the link in above comment.
is there any difference in speed depending on the amount transacted?
only size in bytes matter. you may send 10000
BTC with the same fee as you send 0.001
BTC.
but there is a limit on how small a transaction you can send. i forgot the limit but for example you can not send 1 satoshi to someone.