6.3 and 3.5 mm (or the inch equivalent) connections are electrically identical. Adaptors are very common and should be easy to find.
Classic tube amps like this usually have a high output impedance, which affects dynamic driver headphones but not planars, and relatively low current output, making them unsuitable for low efficiency headphones. Although that varies.
In short, they are most suited to high impedance dynamic driver headphones like the HD800. The Elegia might be a poor match.
I would personally take a JDS Atom amp over the Magnis due to it having slightly better components, and JDS' support being stellar.
Remember that all these are only amps, while your TA-03s has a built-in DAC.
Third party pads are often a lottery since pads are absolutely integral to the tuning of the headphone and need to be more or less a perfect match to sound good.