Assuming that you leave your Bluetooth on all the time on your phone then it should automatically connect when the speaker is turned on & paired with the phone. Provided your phone was the last Bluetooth device that you used the speaker with. Try clearing your Bluetooth cache. I was also having Bluetooth connection issues a few months ago and clear the catch haven't had a problem since.
•Go to Settings.
•Select “Application Manager”
•Display system apps (you may need to either swipe left/right or choose from the menu in the top right corner)
Select Bluetooth from the now larger list of Applications.
•Tap Clear Cache.
As for the NFC you how to find "The Sweet Spot" NFC only has a few centimeter range.