Can I add this to frosting or to cake batter to give it guava flavor??

I have used guava paste in pastries and cakes quite successfully, it cooks/blends well into ingredients either as chunks or blended in. Depending on the texture you would like to achieve with frosting you may be able to blend it enough to add it but would probably have to cool it afterwards so that it sets better and can be worked, I would try with small amounts. Guava jelly might work better, but may also soften the consistency quite a bit. There may be some trial and error involved, but it could be worth a try, the guava flavor will certainly come through. :)

Why did the price go up from $1.16 in December 2020 to $4.22 in January 2021? Really in less than a month!

I was wondering exactly the same thing, I just chocked when I try buy agin and saw the price. Can’t understand why it went up SO much in one month. So, I didn’t buy, and I will not.

Is this product sticky and gooey, or can you cut it cleanly into slices?

This product is very sticky, but not gooey. I've been able to cut it into slices just fine, though handling it can make everything very sticky.

can I use the guava paste if two or three months paste the use by date?

I mean you CAN do whatever you want to do. As long as it’s remained unopened in packaging and isn’t spoilt, might be ok. It’s pretty shelf stable but 2-3 months past expiration is pushing it.