It depends what you mean by 'problems'. The output voltage varies with load current. Check the datasheet for the particular brand of 555 you want to use.
You should use a simple voltage follower (op amp) on the output of the potential divider or digital potentiometer to minimize loading effects. A single supply op-amp voltage follower is easy to construct and will assure that your output amplitude is correct regardless of the load resistance.
Here is my final schematics....(one using OP AMP and other using BJT).
Kindly give me necessary advice on selection between the two ones that is better?
Is there any mistakes in my design and selection of components ?
After getting a clear answer I will go for hardware implementation.
The pot in parallel with the load in the first circuit will not give the required variation in pulse amplitude.
The 741 opamp has an output current of ~25mA max; not enough to drive those loads.
Neither circuit has a way of stepping the output level.
To be able to drive a 33Ω load and the other loads at a controlled 5V you will need a supply voltage of at least 6V, preferably 8V, (to allow some control headroom) with a current rating of at least 150mA. What do you have available? Will the circuit be mains powered? Will the voltage stepping be manual (selector switch) or in an automatic sequence?
Yes, but you said you wanted to have a fixed voltage for the 555 monostable and apply stepped height pulses to a load. What will control the stepping? Each step initiated manually? Auto-sequence?.....?
The purpose is to source 1ms mono pulse to load(33,68,100 Ohms-one at a time) at different amplitudes ranging from 0V to 5V in 0.5V steps by manual adjustment.
I don't think you will get the amplitude steps you want with that circuit......I would suggest the votage divider (as suggested by alec_t) with the voltage follower op-amp circuit to buffer it. You will need to use an opamp capable of the drive current you need or use an emitter follower circuit.