The key word, here is "if." Yes, if the tires are bad, replace them. Being 25 years old does not necessarily mean they are bad.
If the tubes leak, replace them. If they don't leak, don't replace them. There is no need to replace inner tubes that hold air.
Right. I have ridden many thousands of miles on very old tires - tires from the 1960's. If the skins are OK, they will last. Of course, with the old 27" gumwalls, the tan gum sidewalls will rot and looks terrible. That is probably good enough reason to replace them, but it is only the asthetics of it because the tires will still hold up. Oddly, later versions of the 27" tires got rid of the shock-absorbing gumwalls, but kept the look and replaced the gumwalls with synthetic tan colored material which didn't rot (and also did not provide any other real function other than provide the gumwall "look").
I feel that we are responsible for riding tires until they are worn out before we send them to a landfill.