When installing PEX, there are clamps that are supposed to be used to attach it to framing. There are also gaskets for when the PEX passes through openings and such. These are nothing special other than made out of a smooth plastic to allow the expanding/contracting PEX to more smoothly slide.
Sounds like these weren't used, or a few are too tight, or maybe the PEX is just rubbing a little bit next to a structural element.
Is it something to worry about? Probably not.
It's really hard to read your question, but I think you are essentially asking: "Is it okay to replace galvanized pipe and connect it with copper?"
The answer is yes, but there are a couple things to keep in mind:
Copper and galvanized pipe will suffer from galvanic corrosion where they meet unless they are isolated. This requires use of a dielectric union
Galvanized pipe also is generally cited has having a 40 to 50 year lifetime. Generally they will rust from the inside out, restricting the flow in the process.
This restricts the flow, and is often the reason that older homes have such poor water pressure. It would be a shame if you get your new shower installed and then find out the pressure is awful, and it could very well be that it is the galvanized supply lines and not the shower itself.
There is also the possibility that there are metals leeching out into the water supply from this corrosion, but to know if this is happening for sure you'd have to get your water tested.
Once you start seeing corrosion on the outside of the pipes, it's just a matter of time until you have a leak. I've actually hard of some home insurance policies not covering damage from leaking galvanized pipes, so that might be worth checking out.
There's also no reason you have to use copper, pex is a perfectly valid option, and for replacing a long in-wall run it's significantly easier to install than copper (it bends, and comes in spools up to hundreds of feet long).
Best Answer
It appears to me that the copper tubing connected to the outflow of the filter is long enough to reach the saddle valve. ( upper right corner in Photo ? )
If that is the case you can eliminate the extra tubing feeding the inflow side of the filter and just go directly from the saddle valve to the copper tubing that is feeding the refrigerator.
You may be lucky and the threaded fitting on the outflow tubing will be the correct size and kind to attach to the valve.
The saddle valve could be a 1/4" OR 3/8" connection. If you turn off the valve and then disconnect the line from the valve to the inflow side of the filter you can then mark the valve end and the filter end of the tubing and take it to the store so you, or the associate, can determine the correct coupler fitting to use to connect your existing fitting to the saddle valve. ( the inflow threaded fitting appears to be the same as the one on the outflow side. )
If it were me i would replace the saddle valve, they are notorious for failing due to corrosion over the long term. This require shutting off your water removing the saddle valve, cutting out the puncture from the saddle valve and soldering in a Tee, ( or use a push to connect fitting ) Then put a 1/4 turn valve on the tee branch for the refrigerator and the correct fitting to marry to the threaded fitting on your exciting tubing that goes to the refrigerator.