They can change the terms, but if you don't sign the new terms then you have never accepted the new terms.
For some reason, companies think they can write anything into their terms and think it matters. It doesn't. Most contracts aren't worth the paper it's written on.
"By continuing to use the software, you agree to the new terms..." which is, of course, hogwash, but wouldn't stop them from say "Sorry, the new terms were released and you agreed, so pay up."
Depends on how long your license is for. If you have a 1 year license and they change the terms, you are going to have to sign new terms for the next year's license.
Sure, but they also say you can use an old version if you prefer the old terms. Basically, that if they update the terms, it’ll only apply to the current/future versions.
So just stop using the current version. Just use the old version which still has the old terms. You never agreed to the new terms, and under the terms you agreed to, you can continue to use the old terms.
That poses an interesting question. If they can change the terms, and say that you agree to the changes by continuing to use their software, and they remove the clause allowing you to use the previous agreement, then can you use the previous agreement? It's a bit of a buried shovel problem. Have you agreed to not use a previous agreement by continuing to use the software, or can you stick to the old agreement that lets you use the old agreement?