Questions about Patona Sony PSP-S110

Hello, Recently I've ordered PSP-2000 batteries from iFixit, but they were too big to fit inside so I had to shave off the battery a little bit. And the battery life was not the best, mostly 3 hours tops. I see that this one has good reviews, and I wanted to know about your experiences... Does it fit well into the battery compartment? And how is the battery life? Thanks in advance!

Is the battery compatible with the first PSP1000 version (1004)? Thanks

Is this battery also suitable for the PSP 2004? Thank you!