1) Is it possible to log into your wallet from any computer using the electrum software and your seed? For example .. if you went on holiday or your computer broke?
Yes. Your seed will generate all the addresses that is in your original computer, provided that the wallet itself is generated with the seed.
2) If you want to access your wallet using different software on a different computer, what's the best method?
Electrum doesn't use a standardised seed format so its quite impossible to find any other decent wallet that supports it. Electrum does however, support BIP39 so you can get a wallet that generates BIP39 seeds and use it with Electrum. You do need to know the derivation path though, you can typically find it using Google.