My understanding is that PB pipe is perfectly fine, it's fittings that aren't. You can connect PB to PEX but you need the proper transition/conversion/adapter fitting. The OD is the same but the ID is different thus can't use a standard PEX fitting. If it were me, I would take a sample piece of the PB pipe to a plumbing wholesaler and they can set you up with the correct bits and pieces. Don't go to a retail store.
I like copper crimp rings. You can rent the tool at most rental yards. A PEX crimper is large and hard to get into some locations though. I would suggest using a PEX cinch clamp like in the pic below (not a hose clamp). The tool doesn't cost a lot. Sharkbite fittings are fine but will get expensive if you need a bunch of them.
Connections to a faucet, toilet and HWH use a standard "swivel" fitting and you want to connect PEX directly to them and are available in elbow or straight style. Not sure what your line to the toilet looks like but nowadays it's a whitish re-enforced flexible tubing that is typically connected to a PEX fitting with a cinch clamp. I would replace that too (available from an RV parts vendor).
When buying PEX tubing, get it in straight lengths and not in coils. The coiled stuff is difficult to work with because it has a memory and will not straighten out and stay straight. Don't secure/clamp it down tightly everywhere because it does expand and contract with temp. changes. Use a PEX tubing cutter to ensure clean & square cuts. There's also a tool for making bevel cuts when using sharkbite fittings to minimize the chances of a leak.
There a number of ways to connect PEX tubing:
6 ways to connect PEXSome info. on past issues with PB pipe and other types of plastic pipe (ABS, PVC, etc.) here:
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