Is it possible to get any replacement parts? One of rhe bigger rods that connects the band to the clip fell out

You can buy a package of pins and rods of various sizes online from anyone that is selling watch parts. The package is fairly inexpensive. You can even order them from Aliexpress but it will take longer to arrive. Try to get a general length in MM and look on ebay or Amazon for a package that would include that size. I got a package of them when I ordered a watch repair kit that included a lot of tool and a package on pins. Good luck.

How can I find instructions on how to downsize the band?

I BOUGHT the same watch. I have experience adjusting watch bands and couldn't find a way to do it. I paid a jewelry repair shop $12 to adjust it.

Why does it take long to get here? I have to wait 2-3 weeks until I get mine!

Patience. If it is a puppy you're waiting for, it may need to age. if it is shipping from China you didn't want to pay second day air. Try writing a better question to get a better answer.

what size is the battery?

You'll actually have to open the back and look at the battery to find the model number for a replacement. Alternatively, you can find the watch on Aliexpress and look at the specifications listed with the watch, and see if they mention the battery type (I've seen this in some cases). Good luck.