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1. Your standard BB browser and Opera Mini are your choices.
2. Yes. Enable Mass Storage on your Media Card. How do I add media files to my microSD card? - BlackBerryFAQ
3. Absolutely-- How do I edit my notification tones (profiles)? - BlackBerryFAQ
4. You might have turned it off... Phone Dialer screen > Menu > Options > Call Log = set as desired.
If the above is set correctly, you could have low memory issues... Managing your BB Memory - Lost Call Logs and SMS