The problem is that on my balance it says "Synchronizing..." and i found out that this may be because i havent updated. And to update i need to download over again, which means i would need my seeds to recover my account, in my understanding. I cant remember writing down this seed anywhere when i created my wallet, and its greyed out in "Wallet" section. So how would this work when updating Electrum? How can i make sure i wont lose my account and $$? Can i use something else than seed to do this?
You shouldn't need your seed to simply update the application... when you update Electrum, it will not overwrite your old wallet file. I'd still recommend that you make a backup copy of your wallet file ("File -> Save Copy" within Electrum), just in case... then simply install the update. You should find that your wallet opens normally and you can continue.
Also, given that you have lost the seed, you should make a completely new wallet and move those coins ASAP. Without the seed, recovery of a 2FA wallet in case of total wallet file loss is impossible.
I heard something about Private Keys, which i have the option to Export. Will this be my alternative to seed? Can i use this to get to my wallet when i download latest Electrum?
You can't use that method with a 2FA wallet... an Electrum 2FA wallet is a 2-of-3 multisig... you only have one key stored in the wallet, TrustedCoin have another... the 3rd is "stored" in your backup seed (which you don't have).