F serial number is prior to 2003 I . Not sure I can find how far back it goes, tends to be a pretty long run (G I know is 2003 to 2011 or so)
No good tighter dates on the Savages of modern era.
The rest is irrelevant as far as I know. All the marks on the barrel are probably just various inspection, quality confirmation stampings.
As noted, you need to know what kind of bolt you have.
It just my opinion that the safest setup if the modern push feed as gas control is much better. I am just doing my first one, nice to know that you have the best setup for a problem though I don't anticipate one, I like the better feeling when I pull the trigger (Switchgear rifles say do it with a string but that's not doable at a range)
Good luck with the build, I am doing a temporarily install on my 111 with a 308 bull. So far the biggest problem is getting the stock channel down to fit it.
I have a good setup with torque wrench, did the offset torque calculation adaptor etc to get the 3/8 inch torque wrench to fit the 1/2 inch hold in the tool, breaker bar for taking nut off.
It did take a bit of back and forth to get the headspace right, gauges are by far the best way and for sure if you are new to this.
A lot more movement than I thought there would be for small amount of turn(and my labels are going to be sideways, sight)
Just about there with the stock (the 30-06 is a bull as well so it will be good for that one when it gets here)
Savage Shooters forum has a lot of good information on this as well as barrel makers and how its gone.
I am partial to Accurate Barrel in LA and Apache in same area does the barrel work and all good reports. X-Caliber has good reports with no negative.
Criterion was very amendable and reasonable when a guy had an issue with only betting 3/4 MOA so that's another one (some barrel problems seem to crop up but with good customer service that's a key)