Yes, You can connect the MP-CD1 with Apple iOS devices with an Apple Digital AV adapter.
Yes, Sony MP-CD1 does have the HDMI slot and you will get an HDMI cable also inside the box.
Yes, Sony MP-CD1 comes with 5000 mAh battery and it does support the fast charging thanks to USB Type C charging slot. It takes about 2.5 hours to fully charge MP-CD1.
Sony MP-CD1 weight is just about 280 grams.
Yes, Sony MP-CD1 does have a manual focus slider.
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.