When am I ready to face a Dungeon?

Generally, when your first starting out, the special dungeons (depending on what they are) can be much harder, for beginners. Think of special dungeons as special events, which arent always available, and depending on time of the week or year, are available. Depending on what your starter monster was (your first Rare egg machine pull), the special dungeons can be harder or easier. We would have to know your rank and monster box to get an idea if your ready for the special dungeons. It would be wise to get an app called "padguide" It gives you info on dungeons, monsters, events, evo material for monsters and stuff. Think of it as the encyclopedia for the game. You may be ready for some of the earlier variations of the dungeons, such as int, and maybe even expert, if you look at the guide to see if you wont get 1 shotted, or can kill the monsters before that. Although, I would not recommend doing the mythical dungeons for a while, because they are pretty much all tough descends, and even if you do have barely 50 stamina, will be a waste if you arent ready yet.

It depends.

How skilled you are and what monsters you use make a big difference in regards to what dungeons you can likely clear. The stamina cost and difficulty tags for dungeons can be helpful, but cover wider and wider ranges of difficulty as you get stronger. For example, there's a big difference in difficulty between, say, Hera-Ur Descended (Mythical) and Surtr Descended (Mythical), probably bigger than the difference between most Intermediate & Expert dungeons.

In general, your best bet is to use a resource that lets you look at the dungeon before you try it. I generally use PADX, but there are also some good apps out there. Check out what you'll face in the dungeon you're considering attempting. How much damage can you do reliably, to deal with trash floors? How much spike damage can you deal with actives? Are there floors that you can stall on to get your actives ready? Are there any large preemptive hits you need to worry about? What about absorb shields?

From the amount of progress you described, it sounds like you could handle the 10-stamina versions of the Wednesday, Thursday, and Friday special dungeons, and probably the first 1-3 levels of challenge dungeons, but most other (non-gift) special dungeons will be too difficult for you, or offer poor rewards for the amount of stamina and effort they cost. If you keep clearing Normal dungeons you'll eventually unlock Technical dungeons; once you can clear the first dozen or so of those without too much trouble you're probably ready to start attempting some of the easier descended special dungeons.

Note that the 25-cost Wednesday & Friday dungeons are notable in that they consist entirely of enemies with very high defense and very low hit points. You can build a team specifically designed to cheese through these dungeons (use one of the ogres as a leader for the "don't die when a hit takes you from over 80% hp to 0 hp" leader skill, along with a lot of high recovery and low hp subs such as ninjas; an ideal friend is one with a leader skill that either automatically recovers hp or one that boosts recovery). Since they're by far the best place to get certain evolution materials and can be difficult to defeat with a normal team until your cards are significantly stronger, it's often worthwhile to build a team specifically for beating them.

Special dungeons usually have conditions that are difficulty for the general beginner. There are several conditions that you should satisfy before you attempt special events to give yourself the best possible chances of completion.

• If the dungeon requires 10-15 stamina, this event should be easy for beginners (and the difficulty that may or may not be given in the description will mention that it is "Int" (intermediate) or lower)
• If the dungeon requires 16-25 stamina, this event may be difficult for beginners, due to the amount of damage that it does. You should not enter these dungeons until you have (a) at least 500 ATK for 3+ monsters, (b) 7500+ health, (c) can make at least 3 combos most of the time, and (optional) (d) have a monster with multipliers using a leader skill. In dungeon, anything with a "Strong" on top of the monster should be attacked first, as it would either deal too much damage for you to recover from (with future battles) or may be an instant-kill. These dungeons will usually be labeled with "Expert".
• (Note: I have not attempted a dungeon that uses 30+ stamina, so data may be inaccurate) If the dungeon requires 26+ stamina, even experts with the game may have some difficulty with these. These dungeons are usually labeled with "Mythical" or something similar. Multiple monsters with "Strong" may be present in a battle. You will need a large amount attack, a large amount of health, a large amount of multipliers, and a large amount of combos.
• Please note that the above descriptions do not apply for events labeled as Gift. These dungeons are SUPER EASY provided you have even a mediocre attack. The monsters usually do not attack or deal a small amount of damage (100-ish), and you will receive a great reward. For example, the Special Dungeon "Experience of a Lifetime" requires 30 stamina, but awards 200,000 EXP, which is enough to boost you multiple ranks (I went from 28 to 51)