Can haz questions?

[PomPomFlare]

1. Depends. The cheapest I saw is 4 mil.
2. You also can do gathering. (Crafting was supposed above)
3. People say here about undersized party option when you retain your leves and skills but dont get experience for dungeons. Actual runs require party, arcanist evolve into DD or Healer.
4. Raiding or fighting "gods of random" in diadem(added in patch 3.1).
5. 3\10 I suppose. Depends on how to scale it.

[DisFlavored]

1. There are very few plots available at the moment and their price depends on how long they've been vacant. It'd be in the 10 mil area most likely. Your best bet would be to join an FC who has a house. You can then have your own private chambers that you can decorate for 300k. But I do believe you need to be max rank in your Grand Company. (Everything here is heavy story)

2. The best way to make money is usually to gather/craft. You could however pick up some vendor gear and spirit bond them for materia. Crafting/gathering gear would be the best.

3. You can't really solo dungeons here unless, like others have said, you significantly outgear the content. Most of your instances will begin by using the Duty Finder to find a party. 4 man dungeons are 1 Tank, 1 Healer, and 2 DPS. As an Arcanist, you will be a DPS. Once you hit 30 and get your sub class to 15 (depending on what you want to be), you can remain a DPS as a Summoner or become a healer as a Scholar.You are able to obtain both soul stones and change classes as you wish.

4. Best gear is usually killing things. Like raids, dungeons, or exchanging tomes for gear (obtained by clearing dungeons lvl 50+).

5. I guess 3?

[Niwashi]

1. How much will it cost to buy a housing plot? I'm not really going to be picky, I just want a place to call home and maybe afk in. I am in the Excalibur server at the moment.

This wiki lists the price ranges they start at. Theoretically, they then drop in price over time if they stay unpurchased long enough, but on larger servers especially, they tend to get snatched up before that can happen (especially the small ones).
Besides the high prices, though, there's the issue of whether you can even find a plot available to purchase. There's a severe shortage of them, especially for the more highly populated servers.

2. I'm a level 14 arcanist who might want to start making money soon, but anyways, any suggestions on making some decent money? I don't mind if you just give me an option that I can do later down the road.

People have already mentioned that gathering and crafting are big money makers. You will need to advance your arcanist (or another battle class) a few more levels before that becomes feasible, though. The level 17 main story quest "Scions of the Seventh Dawn" unlocks retainers, NPC assistants who do various things for you, such as storing extra items and managing sales of items to other players through the MarketBoard. You'll want their storage before getting very far into crafting and gathering, and can only make money from it once they're available to sell your items, so stick with the main storyline at least that far before deciding if you want to take some time out to work on crafting.

3. How viable is arcanist as a tank or as a solo character? I prefer soloing dungeons since I feel like it makes stories much more awesome (I feel like it sort of takes away from the overall story if you need 7 other random people to fight the main antagonist, but that's just me).

Arcanist isn't a tank, and nor are either of the jobs it can upgrade to at level 30. It does however have a tank pet (Topaz Carbuncle as ACN, or Titan-egi as SMN), plus some healing abilities on a damage dealer class, making it the most well-rounded, and so one of the strongest in the game at soloing content.

While you can go back and try soloing dungeons once you over-level them a bit, it's not going to be very feasible for your initial run, at least not most of the time. You might be able to do that for some of the optional dungeons, but most appear within the main storyline, so you're going to want to do that initial story run when you're on level (or near to it) in order to continue through the next part of the story on-level. On-level, they're not really solo-able.

Do you know where I can claim a white devil mount? I can't find any information regarding where to use the key.

Use the item to add it to the list under "Mount Guide". Use it from the Mount Guide to mount or dismount. Before being able to mount, though, you'll also have to unlock the mount system. Once you join a Grand Company (level 20 in the Main Scenario quest line), do the My Little Chocobo quest at the GC headquarters. It both gives you a chocobo mount and unlocks the mount system in general, so you can also use any other mounts you have.

[Atoli]

I prefer soloing dungeons since I feel like it makes stories much more awesome (I feel like it sort of takes away from the overall story if you need 7 other random people to fight the main antagonist, but that's just me).

If warriors can solo fights I might decide to switch, maybe once I master arcanist, who knows.

When people say Warriors can solo pretty much anything, that's refering to very few people who know insanely well how to time their skills, and who also are at max lvl and close to max gear level.
And even then, it still only refers to "old" content, not the current new stuff. Just get used to the thought that you are not supposed to solo instanced content when you do it for the first time. The option to go solo is so you can later go back without having to share the drops and stuff like that. Obvious evidence is that 1. you can't clear the content solo unless you outlevel it by A LOT (and somewhen you hit the point where you can't outlevel content anymore so you will get stuck if you refuse to do it with others) and 2. you don't get any experience or anything unless you run in a normal-sized party.

But don't worry, it won't really take away from the story
You are still treated as the sole hero of your story. Not going with other adventurers would actually be weird because the story keeps referencing them (basically saying "hey, take some of your friends and rid us of that monster problem!").
But when you are in an important story cutscene, you are pretty much the only one who shows up, so you will still be the awesome one

[bounddreamer]

There are two jobs that are great for solo play: Warrior and Summoner. You'll be able to get most of what you want done with either of those two jobs.

However, every dungeon and instance you need to clear is wither four or eight man parties, and those are tied to the main scenario, so it's mandatory.