Question about low voltage wiring for LED lights (not truck related)

I've been having a hard time even figuring out how to ask this question via google, so I thought I'd come see if I could get a hand over here. Lot's of folks on here who understand how the magic of electricity works...

I've got four of these 'starburst' lights from Amazon:

FOOING 4 Pack Firework Lights Led Copper Wire Starburst String Lights 8 Modes Battery Operated Fairy Lights with Remote,Wedding Christmas Decorative Hanging Lights for Party Patio Decor (Blue Pink)

https://www.amazon.com/gp/product/B08GYH6JR6?noLL=1&askMessage=GENERIC_ERROR&th=1

Each one runs off of x4 AA batteries. They have different modes so there's a little controller in there too.

I have a few related questions:
1) Can I cut the wires to splice in an extension? I'm only trying to extend like 10', so I don't think I'd need to be concerned with voltage drops. I am concerned about the control function though (for the modes like 'blink', 'breathe', etc.).
2) Can I splice all four of these light fixtures into a single AA battery pack? I know the batteries would drain four times quicker, but I am only planning for 2-4 hours of usage.
3) If I'm already going to all this much trouble, can I use something with more amp hours? Like maybe replace with x4 14500s? I'm not sure if I'd need additional hardware for battery management.

And now that I've got that all out there on the table... would it have been easier and cheaper just to make my own little version of this product? I've never worked with LED lights but I've learned a good bit about splicing wires together on my tundra's house battery.