While there are a number of no-name options (most of which are not MFi approved, and may cease to function at any time with future iOS updates), the only one I’ve seen that’s from a vendor I’ve heard of is the Belkin 3.5mm Audio Cable with Lightning Connector.
That will work too; it’s a question of how many connections you want vs. total cable length.
I’m not aware of any Lightning-to-2.5mm Balanced cables/adapters.
Digital only from the Lightning port.
Which means all of these cables, and any similar adapters, contain a DAC (and most also have an amplifier), as the 2.5mm and 3.5mm connections are all analog.
If you use an external balanced DAC on a USB connection, yes.
USB Audio, which is digital, has no notion of single-ended or balanced … it’s just concerned with the data. It’s up to the device receiving that data to convert it to analog, and whether it does that in a balanced form or not.
Usually you’d just be looking at a USB “dongle” DAC. Almost all of those have 3.5mm TRS outputs. I don’t know of any balanced-output “dongle” DACs.
Depending on what headphones you’re driving, you may be better off with the iFi xDSD, as that can connect, digitally, directly to an iPhone with the simple Apple Lighting-to-USB 3 cable, is an excellent DAC with a more-than-decent headphone amp and that has both balanced and single-ended outputs.
With the xDSD you also have the option to feed it via Bluetooth from the iPhone in cases where you don’t want to deal with cables. Though running it wired is definitely preferable.
Another option, without the Bluetooth capability, would be the iFi Nano iDSD Black Label.