Is it possible for a wilder to lower his manifester level after
unsuccessful psychic enervation roll to suffer less damage or the
option to lower his manifester level must be made at the start of
manifesting and a wilder cannot changed it after.
Where are you reading this, specifically? I don't think I've ever heard of rules in Pathfinder which mentions anything like this. No, you can't change what level you're manifesting a power at after you have already decided prior to invoking surge. If you make the option to manifest a power without paying power points and you enervate because of it you suffer consequences equal to your manifester level.
In other words, you flubbed your casting and due to the rules involving invoking Wild surge without paying for power points, you have to wait ten minutes until you can make another attempt to manifest without power points again.
A warrior wilder overcome by psychic enervation is staggered until the end of her next turn and loses a number of hit points equal to her normal manifester level (the increase in manifester level from her wild surge does not increase the number of hit points lost).
In this instance, you'd lose your manifester level (equal to the number of class levels in a given manifesting class) in hit points. If you're a Wilder 3 your manifester level would also be three. If you were a Wilder20, your manifester level would be 20.
Your manifester level can be augmented. The level at which you manifest a power changes depending on whether or not you used the Overchannel feat, or whether or not your Wild surge was successful. But your unmodified Manifester level is always equal to your number of class levels in psionic classes.
Instances in which increasing your manifesting level are important when utilizing the power Dispel Psionics (/Magic). In this instance a higher manifester level increases your chance of dispelling magic or psionics.
Using Overchannel can increase your manifester level by up to 3, and in doing so increases the maximum amount of power points you can expend on a power by 3 as well.
If you try manifesting the power Minor Metamorphosis with no power points, using your psionic focus to do so, and suffer enervation, the effect of your Warrior's Surge enervation takes effect and you lose Three hit points.
On that flowchart, directly at the end of the branches stating "The Wilder is overcome by the strain of her effort" you would add the section where penalties for Enervation are calculated.