Thanks for posting on Adobe forums. Unfortunately, that's not a feature of Lightroom mobile yet. That's a great feature to have on Lightroom for iPad. I'd request you to share it here Photoshop Family Customer Community so that our engineers can look into it.
2. How can I sort them differently (other than chronologically)?
If you tap the gallery heading there is a sort command at the bottom of the menu, with multiple choices.
If you want to manually rearrange, press and hold any image and a menu will pop up. Tap Change Order, and then press and hold an image to enable dragging. To move multiple images, tap them first, then press and hold to drag the set.