Can it be kept like this in the long term?
Yes.
Will it affect transmission speeds?
No, there are no capacitors in the circuit that is the only thing that would affect the transmission speed.
Tx ---1K8---3K3--- Rx
No
TX --- 1K8 --- Rx & 3K3 --- ground
it would mean that the arduino pro mini understands the 3.3v logic on Rx!?
There is sufficient voltage on the 3V3 output for the 5V input to recognise it as a logic one.
What is strange is that i different way to do that,
In electronics there are often many ways to solve a problem, this is none of them. The advantages of simplicity are balanced against the fact that the noise margin is worse and the impedance is higher. However it will work. Do you want to do it cheap or right?
did you already give it a try with an arduino promini or with another arduino
I have used this technique for converting logic levels but not used it in this specific configuration. This should not be a concern of yours.