1) If my phone were to explode and I needed to restore my wallet, do I need to use the same wallet? Or can a seed phrase I got from mycelium be used in electrum if I wanted?
That depends on the developers of the wallets.
There are some wallets where the developers have all chosen to use the same word set and seed generating algorithm, there are others that have decided to implement their own method.
As long as the source code for the wallet is publicly available, or the wallet developer has published their word list and algorithm, it should be possible to regenerate the necessary private keys to import into some other wallet. It just might not be very easy to do if there aren't any other compatible wallets already written.
2) Is there no risk of people just randomly entering 12 word seed phrases in the hopes or recovering an active wallet with funds in it?
For all the well written wallets, the number of possible word phrases for the seed is astronomical. A properly generated word phrase should be as secure against being "guessed" as a valid bitcoin private key for the given address.
