Here is my opinion. Last season I climbed to diamond with zyra mid and sometimes zyra support.
Zyra can potentially output a huge amount of damage. The problem is that she is squishy and has one of the slowest movement speeds, so if you go behind you tend to lose more games at this point. I think people prefer morgana In Support or orianna in mid as replacements, because with morgana that Q can always be relevant and orriana can provide better utility as well as damage. I don't want to elaborate too much on this topic however.
Although seeds can be used for vision, that vision is too inefficient to be able to see ganks coming fast enough. the general rule I go with on first buy is that if our lane has the advantage, upgrade spell thief, then get sightstone. Otherwise, try to get sightstone, since the health can be quite valuable. depending on the amount of gold you have, I also recommend prioritising two health pots and one mana pot, then getting items. For example, between 800 and 1000 gold, you might want to consider boots + ruby + at least one green ward + pots, as opposed to sightstone, since the movement speed is good with lane control.
Spell order looks fine, depends on the game and how you want to play it out. I have tried maxing Q and maxing E first before. I prefer Q for higher poke damage, but a longer snare on E can also be more useful.
With combos, I have the habit of trying to snare first because I want to make sure that the R knockup lands. I do see the logic in your combo however, Since after the E your Q is probably going to be up again. I just think the positioning has to be quite spot on, since zyra stops during q cast and stops again during r cast, so there is a good chance imo that they will either be out of range for an e and/or be able to walk out of r.
Rylais, although expensive, synergises pretty well with liandrys, so on zyra support I would get that over Athenes. Also I this new patch, I haven't tested it yet, but I think banner of command could be a good pickup, since it gives AP while still providing the aegis passive.