[cypher]

Thyme should be ok but only in very small amounts, it's sometimes used if a ham has a cold, chives & garlic chives are onion family so definitely no, mustard leaves no, I could be wrong but I think Cilantro is rocket? if it is that's ok in small amounts, sage, dill, basil & marjoram should be fine, parsley is generally ok, not sure what Italian parsley is exactly but I'm pretty sure all parsley is fine, not sure about summer savoury is I think quite similar to thyme so ok but both have quite strong medicinal properties so again only tiny amounts.
Most likely to be eaten are probably basil & parsley.
How are you planning to grow them in the tank?
It's a nice idea but doesn't often work well, plants need plenty of light, water & something to grow in with nutrients you probably won't want your ham to eat. Plants in a tank can cause damp & condensation build up which could lead to mould in there, not nice!
I find it best to grow things on the window sill or somewhere light & airy & just put them in the cage for short supervised periods & generally only give "weed" that don't need fertilised compost to be safe.