Electronic – arduino – Is a N-Channel Mosfet save/reliable for level shifting UART from 3V3 to 5V

For unidirectional data flow, although there will be shifters more suited to lower voltages, you should be fine with this chip. On page 6 of the ST datasheet, there is a High voltage vs Low Voltage graph which indicates a minimum combination of ~3V for Vcc and 5V for Vdd:

If you are using both Rx and Tx, then you will need a bidirectional level shifter, such as the ADG3304. Or you can use two unidirectional ICs, as discussed in the comments.

Steps to design:

1. The collector current of the transistor is given by $$I_C=\frac{5V-V_{D1}-V_{D2}-V_{CEsat}}{R_2}$$ Where \$V_{D1}\$ and \$V_{D2}\$ are the forward drop of LEDs. \$V_{CEsat}\$ is around 0.2V for BC547.
   So first fix the value for \$I_C\$ by selecting a value for \$R_2\$. The value of \$I_C\$ must be less than the maximum collector current of the transistor (100mA).

2. Find the base current of the transistor as: $$I_B=\frac{I_C}{h_{fe}}$$ This is the minimum base current required to place transistor in saturation. From the circuit, $$I_B=\frac{3.3V-V_{BE}}{R_1}$$ Where, \$V_{BE}\$ is 0.7V.
   So design \$R_1\$ such that \$I_B\$ is sufficient to make the transistor put into saturation.

High current flowing through the LEDs can reduce the life time. So choose \$R_2\$ wisely. The datasheets of LEDs will give the current ratings.