With #1, if that exchange or online platform relies on, uses a Payment processor from another company like Bitpay, that has problems temporarily, you will not see your transaction, deposit credited to your account. Contact their support service to fix it.
The company can wait for BitPay for example to fix problems and broadcast transactions, credit deposits automatically or the company can broadcast, credit it manually for users in waiting time of problem resolve from BitPay.
Payment processor has nothing to do with this, this doesn't involve crypto to fiat transfer or conversion of x crypto to y crypto. It's just moving Bitcoin from A to B and I guess OP meant crypto wallet as this platform
cryptowallet which offers multiple services including buy/sell/swap but these detect the transactions as soon as it reaches certain number of confirmations which is generally varies from 2-6 on most.
So OP sent funds with low fee which caused the delay and there is no point is speculating any further unless OP shares TXid or such details.