1. Don't get me wrong, I play SMN and I like SMN. And generally the feeling I get when I play my SMN is that it's somewhat close to my RDM from XI. I like it more in some ways and less in others.
And yes, basically every job has DoTs, but the only job that gets their identity from their DoTs is SMN and SCH when you aren't healing. I mean, your Egi is just a persistent DoT spell that has a couple of extra features. If anything, I'm fine with calling my SMN an ACN instead because then it doesn't disappoint people who get too hung up on how THEIR SMN is supposed to be instead of just playing the job if you like it. If anything SMN is the proof that labeling matters to FF players. At least the ones that like to complain. While I want RDM, I don't want to make something called 'RDM' that isn't new or interesting just to be able to say that RDM is in the game. It would be better to design more diverse jobs that improve job choices and see if RDM is appropriate for one of them. If not, call it something else that is more appropriate.
I don't think they can make another DoT job without it being a rehash of Bane, Fester, and Contagion mechanics. If you look at BRD they literally just added those concepts to BRDs DoTs in the expansion. Another ranged caster that uses DoTs probably won't add any variety to the job line up.
2. There should be redundancies in what roles are filled by the various jobs since a full party has 2 tank, 2 healers, and 4 DPS. However those jobs shouldn't fill that role in the same way. The limit break gauge is intentional designed to foster this idea. MNK, NIN, and DRG all fill the role of a DPS and are melee, but their support abilities and the challenges that they face to get ideal DPS for the party are different. You pick the one you like to play, which you think will perform the best, or whichever one goes with the rest of your party comp if you are organized. I do personally find most of the DPS to be somewhat redundant at this point but they are making decent progress with what is being released in this expansion. They still might be cookie cutter, but it looks like it's getting better.
I'm not trying to get snippy but your description sounded like a current SMN, but without a pet. That sounds like less of a job than even current SMN. "a DoT job akin to summoner with light buffs, cures, and nukes" doesn't sound like it would play any different than SMN. It needs central mechanics that give it different advantages/disadvantages like Ninjitsu, Greased Lightning, Jumps, Astral and Umbral phases, Aetherflow. All of these require some kinds of maintenance to use effectively and if not used effectively, the job plays poorly.
RDM only had 1 thing that was uniquely theirs in the entirety of all the FF games they were in, and that is Dual Cast. That being said, Dual Cast only exists in games that have job systems and would then be taken and used on other jobs and thus RDM was a stepping stone for higher tier mages (FF5, FFTA, FFTA2). In FF3, they didn't have Dual Cast and were generally weak compared to almost every job and you generally moved on to something better. In FF1 they were solid because you couldn't change your party once you started and the job could auto attack deal reasonable damage while conserving MP, nuke to increase damage and hit elemental weaknesses by using MP, and cure. Jack of all trades was a strong and unique option because of flexibility in an otherwise inflexible job system. FFXI made RDM into something different but ultimately failed to deliver a job that balanced to the point that they were either required or useless depending on the content and expansion you were playing. Enfeebling was great in XI until they just turned it off one day and didn't give RDM anything else to compensate for it's loss.
If RDM doesn't have anything unique to offer a party or a unique play style, then I don't want it in this game. It would truly be a disappointment. Looking at what jobs the game has and doesn't have, I'd personally opt for RDM to be a Melee magical DPS. We have ranged magical DPS and physical DPS and we have melee physical DPS, but we don't have melee magical DPS. The point of them being melee is that they would have buffs and mechanics that would use you as the AOE point for their effects. I would love to steal Runic from Celes in FF6 and make it like the Anti Magic shield from the Midgarsormr fight or Flare Dampening from T13. You'd have to cover your allies with the shield so there would be risk/reward (avoid boss' frontal cleave, don't group up on the pepperoni, etc). I'd want them to have to use Runic effectively to replenish their MP so they could use higher cost nukes to increase their DPS. Some level of Enspells or Sword Magic from Mystic Knights would be a good start for keeping baseline DPS while dealing magical damage. You can fight melee with a sword/rapier/longsword/pointy-object with Sword Magic up with a TP combo for sustainable DPS or you could use a magic combo that uses MP instead of TP that deals more damage, but isn't sustainable. I'd also want Dual Cast/Double/Triple that I could cast on myself and others for extra boosts. I imagine that they are planning on adding double/triple to the game at some point for players to use and RDM could be a pretty solid fit. I'd love to be able to pair up with a BLM or SMN and have them do Double/Triple Flare or Ahk Morn/Deathflare or with healers for multi - Adlo or Medica.
I don't care if they call this Mystic Knight instead of RDM either. I just want something different than a bland caster RDM that doesn't bring anything to the party that someone else can already provide. I did that in FFXI, it wasn't very fun when the job became less desirable because it was easier to cripple RDM instead of rework enfeebling to balance the game. Enfeebling in this game is already a joke. Stuns, Silences, and Slows already don't work on ANY Boss worth mentioning. I don't want to set myself up for that happening again.
3. Yeah they do that. The good news is that means a job can do both physical and magical DPS. For all the jobs that are physical, their weapon's magical damage is roughly half of what an actual magical weapon would have at level. We can test this only because cure/physic is able to be used by jobs that aren't caster. There are no actions that are physical that can be used by casters so it's not really possible to know if they truly have physical damage stats or if their auto attack damage is generated solely by the auto attack stats and that they scale with STR and Det.
What does this mean for RDM? Well if you are pro-melee it gives you a niche to explore since you could do both physical and magical DPS. If you are going to be a caster it doesn't change anything.