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1) In the case I never updated my cold wallet version for, let's say, a few years, what would happen? Could I simply download the new version and recover my money by using the seed generated with my n-year-old version of Electrum?
as far as i know you don't have to update every single time they release a new update you can always check the change log (release notes) here on github:
https://github.com/spesmilo/electrum/blob/master/RELEASE-NOTESto see what has changed in the new releases.
but in case of a big change for example from 1.9.8 to 2.0 it is better to update because of the changes they make.
but again you are able to use the old version as cold storage because it can make you private keys and that is enough to have access to the balance no matter what changes, you can import those into any bitcoin wallet and use bitcoin.
and to answer your question you can always down the old versions here:
https://download.electrum.org/ and use your seed from that version to recover your wallet
2) If I regularly update my Electrum version, is the seed always valid? My concern is that, at some point, the old seed wouldn't be recognized and the wallet would get compromised.
as for seed, you should read the documentation and the RELEASE-NOTES to see what has changed in the new versions.
again as an example from 1.9.8 to 2.0 how seed works has changed so the new wallet is not compatible with the old but you can upgrade the wallet and still use the seed.
see the documentation and also this for upgrade:
http://docs.electrum.org/en/latest/faq.html#how-to-upgrade-electrumimportant p.s.
* always make sure to keep a copy of your wallet and seed in someplace safe just in case something went wrong with the upgrade.
** also as i said it is good to know that with private keys you can do anything you want so you can even export the private keys and then mess with the wallet and even if you ruin something you still have access to your funds.
*** keep seed, copy of wallet, private keys in safe place!