Exactly what was her purpose and main objective goal with the flying laboratory?
Earhart's main objective with the "flying laboratory" was the same as it had been with her previous aircraft - self promotion - but 1937 the record-setting, long-distance flying game was getting stale. Just flying someplace wasn't good enough any more. The "flying laboratory" thing was mostly a marketing gimmick and a way for Purdue to justify funding the purchase of the airplane. They did make some attempt to take samples of the upper atmosphere to determine if any insects and bacteria were present. This involved Noonan putting out a pole with a screening device on the end. The pole was held in place by mounts just outside the cabin door. In Earhart's notes for "World Flight" she makes reference to Fred "going back to catch a bug." AE also talked about being interested in the effects of long distance flying on the the human body and I've seen references to her having a selection of sunglasses with her.
...why anyone would leave a life raft behind. It's just not logical in my books!!!
Ah, but you're not thinking like the early long-distance flyers. Lindbergh carried neither parachute nor life raft. In long-distance flying, weight was paramount. The more survival gear you carried, the greater the chance that you'd need it. AE and FN had to know that if they came down at sea and survived the ditching, their chances of being found before they died of thirst or exposure were almost nil. Itasca had no search plan in the event Earhart didn't show up. Earhart never asked that they have one. She seems to have accepted the fact that, just as with her previous flights, the price of failure was death - and she was right.
In 1928, prior to being recruited for the Friendship flight that catapulted her to fame, Earhart wrote a now-famous poem that seems to provide some hint about her priorities:
“Courage is the price that Life exacts for granting peace,
The soul that knows it not, knows no release,
From little things;
Knows not the livid loneliness of fear
Nor mountain heights where bitter joy can hear
The sound of wings.”
It's a theme common in literature. Shakespeare's Julius Caesar said:
"Cowards die many times before their death.
The valiant never taste of death but once."
We can all accept and even embrace the sentiment but we vary in the degree to which we apply it in our own lives. What was it that Amelia Earhart was willing to risk death for? Fame? Fortune? Or was it "release from little things"? I think it's a fascinating question.