LED panel psu and rechargeable batteries

Hello,

I'm new to the forum, what a great find! I can glean some insight from you all.

I want to populate an area appr 1.5" - 2" diameter on a board with 5mm LEDs and drive this with batteries, and be able to recharge the batteries with an off the shelf DC supply, like a 5v, 6v or 12v you use for home electronics. It would be nice to also run this off the DC supply and only on the batteries when needed.

The number of LEDs in the array are not a given, and could be in parallel or parallel\series. I have a 32 LED flashlight, and it is about the size I am suggesting, so the qty may be around 32-40ish. They are not all the same LEDS, the values vary slightly.

Here's the specs:

Forward Voltage VF max 4.0 typ 3.6 V
Continuous Forward Current 20 mA

Forward Voltage VF max 4.0 typ 3.7 V
Continuous Forward Current 30 mA

Forward Voltage VF max 4.0 typ 3.5 V
Continuous Forward Current 30 mA

I would appreciate your ideas on

1) the ability to drive these from a regulated external source as mentioned

2) the ability to run this off of rechargeable batteries

3) the ability to drive a mix of LEDs with the least amount of resistors, for instance, do I really need 1 resistor per LED or can I bind 10 of them through one resistor?

4) if I use batteries in parallel to handle the load, what consideration would I need to use in making this rechargeable without zapping the LEDs? Can I recharge them if they are in series at all?

I know this is a bit much, but maybe I can some insight on one part at a time and piece this together.

THANK YOU for your time and efforts!!

Cheers

.