Yes, both "de" (in the usages I mentioned above) are in the neutral tone (i.e. they are toneless, but the lack of tone is called a "tone" for some reason!).
Both 的 and 得 are indeed very common. Whether or not they are the "most" commonly used words, I can't say, but they are two very fundamental words.
The use of 的 for possession IMHO is the correct way. Measure words do exactly what they say: "measure". Hence, using them as possessives is either wrong, OR dependent on region (perhaps it is a common practice to do so, say, in Taiwan, or Malaysia, etc., but the standard is to use 的 - hence it is what is taught in texts). Basically, the only place one should find a measure word is between a number and a noun, or between a demonstrative pronoun (i.e. "this" 这 and "that" 那).
In Cantonese, it is very common (and acceptable, if not correct) to use measure words as possessives, so it may be a result of a native Cantonese speaker trying to speak Mandarin that measure words are being used possessively. I'm no expert in Mandarin, but based on what I've learned, this is the best answer I can think of.
"wo de ai": I have no clue what this is! :) Here are some guesses:
1. 我的爱 which I would personally interpret as "my love", though I'm sure there is a better way of saying this;
2. 我得爱: which I would interpret as "I have found love", because when pronounced in the SECOND tone, de2, 得 can mean to attain or to reach or to catch. A common example of this use is 我得病=I have caught illness="I am sick".
Check with a native speaker to verify exactly what "wo de ai" means, as mine are nothing more than guesses.
If you want FURTHER confusion, there's also a THIRD "de", which is the structural particle 地, used to modify a verb adverbially, eg. 他块块地过马路=He quickly crosses the street.