According to bulbapedia, trading affects friendship level differently for each generation of the game. I will outlay it in each generation below:
First Generation: Trading will reset to 0
Second Generation: Trading will reset to 70
Third Generation: Trading will reset it to base stats (usually 70 or 140, full list here)
Fourth Generation: Trading will reset it to base stats
Fifth Generation: Trading will reset it to base stats
Thus, no matter what generation the trade is completed in, a freshly traded Golbat will not evolve upon a level up.
Stats other than happiness, such as Effort Values (EVs) and Individual Values (IVs) will however, be preserved.
There is no way to manipulate this. Stats are affected by 5 things:
- Base Stats
- Nature
- Level
- IVs
- EVs
Base stats are always the same for the same breed of Pokemon. Abra will always have a base speed of 90, and Kadabra will always have a base speed of 105. Note that this number is relatively meaningless on its own, but can be used to usefully distinguish relative stats of different Pokemon. The base stat is tossed into an equation to calculate the current stat.
Nature is always determined at the time that the Pokemon is initially created. It either has no effect on stats, or increases one by 10% and decreases another by 10%.
The Level of the Pokemon is obviously included. The higher your level, the higher your stats get.
IVs are set per individual Pokemon. They are randomized at the time that the Pokemon is initially created, and can never be altered. They are an invisible modifier, so there is no convenient way to check them.
EVs are acquired by battling with the individual Pokemon, or by feeding it certain berries. This is the only way to customize stats after the Pokemon has been initially rolled. It is worth noting that you will only see changes to stats based on EVs when you level up. This can make it appear that you are getting a huge boost to your stats if you do a ton of EV training between levels. This may be the effect you are describing.
For more information on how these things are combined into the actual value of the stat, see Bulbapedia's article on the formula.
Best Answer
Unfortunately the Pokemon is considered 'traded' if the Trainer Name/Trainer ID & Secret ID does not match your own.
You can breed it with a Ditto by placing both Pokemon into the daycare, collecting & hatching the resulting Egg, and instead raise the child (which will have your Trainer values). Unfortunately it is male - if it were female you could breed it with any Pokemon in the Field Egg group.
Otherwise, you could try restarting the game countless times in order to try and randomly get the correct Trainer ID, although the odds of getting the exact values is like trying to win the lottery. I don't recommend you try this.