What will happen if we don't bypass capacitor at pin 5 of 555 ic as an astable multivibrator.Will voltage/current changes in line affect on pulse width?will capacitor at pin 1 discharge late?
pin 5 of the 555 is "control voltage" a tap on the divider chain that sets the levels for setting and resetting the internal flip-flop.
without a capacitor there the thresholds will tract the supply voltage exactly ad a glitch on the supply (a brief spke or dip) would cause the threshold to move leading to early triggering of the flip-flop - so without the capacitor on pin 5 supply noise can cause your 555 to run fast.
Putting the capacitor there stiffens the voltage there with respect to ground, and if the timing capacitor is also ground referenced gives a large amount of immunity to supply glitches,
so to answer your questions:
Will voltage/current changes in line affect on pulse width?
yes absolutely, depending on the timing of the voltage changes they may cause the pulses to begin and/or end early
Will capacitor at pin 1 discharge late?
Pin 1 is ground, it's unclear which capacitor you're asking about, because they all connect to ground.
pins 2 and 6 are the timing pins, the charge/discharge of the capacitor there can be triggered early by glitcing the power supply. it can also be delayed if the glitch goes the opposite irection but that effect would be a smaller effect.
Depends on the Ground and VDD inductance.
The original circuit (Signetics) 555, in bipolar technology (schematic of original design shown on "Wikipedia 555 timer IC"),has current limiting in every path except the output driver.
All other paths are either resistor_limited or are actual current sources.
Be safe, be able to ignore that cross-conduction glitch of the output driver; use 0.1uF between VDD and GND pins.