I need to send some bitcoins, but Im not sure how long I must wait. I thought it was safe when the first two transactions disappeared, but that wasnt the case. Based on what happened before, Im assuming if I try again, the same thing will happen, since there is still an unconfirmed transaction. So how long should I wait before I try again? When will the double spend transactions disappear from my wallet?
Only blockchain.info knows. I suggest you contact their support and ask.
I suggest you move to proper wallet software like Bitcoin Core. It may be burdensome considering synchronizing and hardware use, but at least you can be sure that transactions are working 100% as intended. Normally 2 days wait time should lead to automatic reappearance of transactions with insufficient fees. Blockchain.info seems to be mixing things up here.
I didn't want to deal with backup, but this situation makes me consider it. Where is the best place to find out about using bitcoin core?
On
bitcoin.org.
Particularly, you should look at the
requirements and warnings page.
In my view, the easiest thing to do is get a hardware wallet like a
TREZOR. You get very good security without having to back up files or anything - the written seed, which you hide, lets you recover the wallet if you lose your TREZOR. You can also have a passphrase, which is an addition to the seed which means that
even if someone has the seed, the TREZOR and the computer you use with the TREZOR, you can be safe. In fact, you can have a decoy passphrase which you lead criminals to in the case of a 5-dollar wrench attack.
You can use it with several popular software wallets like
Electrum, which you could also use on its own.
If you want security on a different level though Bitcoin Core is a great choice as running a full node can help to secure the network as a whole rather than just you.
Good luck moving away from blockchain.info.