Yes, You can connect the MP-CD1 with Apple iOS devices with an Apple Digital AV adapter.
No. Sadly Sony MP-CD1 does not have the Bluetooth™ connectivity.
Yes, Sony MP-CD1 can work with Amazon™ fire-stick™ and you can connect external speakers for a better sound experience.
It takes about 150 minutes to fully charge the huge battery of 5000mAh of Sony MP-CD1.
Yes, Sony MP-CD1 does have the 3.5mm headphone jack.
If you do give impromptu presentations and don't want to depend on the quality of tech you find in offices and hotels, the MP-CD1 (preferably outfitted with a small portable speaker and a wireless dongle) will do the job. If you aren't a traveling business person and you're looking for a projector with a bit more brightness, you're best served looking at full-on home theater projectors.