First normalize to -1dB which is the default. Use function normalize.
Then lower it about 18 with amplify. Again that is in function amplify.
Next compress it 2.5x1 ratio in function compress.
Then check that the make up gain brings you to -1dB else normalize again.
Yes, this is possible. I've used MP3 Trimmer which does this. However, the result was unplayable in some programs (no audio after the first point in the file I edited), so I ended up reencoding anyway.
These spikes are high frequency components contained in the resulting signal decode. There are two possible reasons for this.
Method one uses a low pass filter which removes these components.
Method two has a decoding fault.
Both of these suggestions are speculative as there is no reference signal to compare.