Gretch,
Yes, you should absolutely detension your bandsaw each day. This will prevent flat spots on your tires, premature blade problems, and prolong your shaft and motor bearings.
Back to chainsaws:
By retensioning as the chain warms, but not when it cools and shrinks, you put unnecessary strain, not just on the chain links themselves, but also on the bar, the nose sprocket, and the drive sprocket as the chain pulls tighter still. Since I cut more than 6 cords a year, I put a new drive sprocket on each saw at the beginning of every season as normal maintenence. I also grease the nose sprocket often (that's what that pinhole on one side of the nose is for).
I've seen lots of problems with sloppy chain sharpening; I've had several mower shops and even a "sharpener guy" completely ruin chains because they would not take the time to do them right. In fact that's why I got a good bench-mounted variable axis chain grinder, and do all the chains for my group of friends because I'm very careful to get the left and right cuttersets precisely balanced, the angles right, and the rakers at the proper depth. This way the chains cut straight and put the same force onto each of the bar rails. A properly done chain and bar should almost self-feed into the wood. I see someone "pushing" a saw into a log and I usually find a dull, improperly sharpened, unbalanced, and/or improperly tensioned chain. Keep working that way and you will toast the bar and drive sprocket as well.
Gretch, all this is not a matter of "caution," it simply makes the saw work much better which is the whole point. I have an arborist friend who borrowed my 28" Husky 372 once. Came back shaking his head (smiling) and went out and bought himself one. Then he came over to my shop and watched how I sharpen / tune my chains. Says once he became aware of the slight error in his grinder's set-up, he's been able to increase the performance on all of his saws with just a little more time. It's not secrets or rocket science. Most of what I do I've gotten from owners manuals [ 😱 ], and manufacturer's literature with a few "old hands" [my grandfather and others] and some trial and error thrown in for good measure.
As far as that old bar goes, if it's toasted and spread or flawed, pitch it. It'll only cause more problems. If it merely needs to be dressed, you can do that youself on your bench grinder, and have a perfectly serviceable bar. If your "old" chain has gotten too short in the teeth, pitch it. If not, learn how to sharpen and balance the cutters carefully.
Try it, you'll like it.