1. I am using this MCU STM8S003F3. Datasheet says dont need to conenct 10K pull-up on reset. So option B in image below
2. In demo board they have option A, but 10K is not mounted.
3. But i have noticed some times their MCU dont start, i doubt placin 10K would be better? Which is ok?
Or option C to be used, it may limit any inrush current.

4. What is more preferable?

 

It's not really required to pull up the reset pin. But a decoupling capacitor should be present as shown in datasheet. I have made a few circuits with the stm8s003f3p6 and I didn't use any pull up resistor, but there were no issues.

 

It realy depends on the application and what else is connected to RESET line.

External resistor (most common 10K) is always being used on devices that gonna pass EMC/ESD tests.

Demo/Evaluation/Discovery boards are designed for starting applications. Sometimes they dont follow their own design guidelines.