Barbarians: You are getting attacked by so many because of where you are located. There is a large unclaimed area to your south, which is prime spawning ground for barbarians. There's not really much you can do about this. Settling into the jungle would cut down on the area in which the barbarians can spawn, but would kill your civilization (trying to support unproductive cities is a bad idea).
Workers: You don't have enough. You should usually have at least 1.5 Workers / city - unless you are playing an elven civ, in which case you should have more. Elven Workers develop improvements slower than human Workers, and also elves develop Forested tiles, which takes longer than developing a bare tile. For five cities you should have no less than 7 Workers, and because you are playing an elven civ it would be best to have at least 10. Currently you only have 2, and this is hurting your growth potential and economy.
Experience: Your army size is reasonable (for 5 cities I would suggest at least 20 units, you have 21), but very under experienced. However, your 21 units only have a total of 24 experience, which is surprising if you've been enduring waves of attacking barbarians. Try to attack the barbarians, rather than just letting them die on your cities, so that you get more experience from the fight. This can be hard with so many Forests around, because the barbarians will have a defense bonus when you attack. You will have losses, but the units that survive will be much better promoted. Try to soften up a barbarian with an unpromoted Warrior first, and then if it dies finish the barbarian with an experienced unit (to reduce the casualty rate of your experienced troops).
Apprenticeship: One of the advantages of researching
Education early is the extra experience you can get from the Apprenticeship civic. One of your unpromoted Warriors attacking a barbarian Warrior in a Forest has a 27.5% chance of victory; with +2 experience used to purchase Combat I, the odds increase to 38.3% - still poor odds, but a significant improvement.
Hunters: Hunting is much too expensive a tech to justify researching just to unlock one Ivory plot. You should definitely have one city (the one with the highest

output, generally) that builds a Hunter's Lodge and produces Hunters. An unpromoted Svartalfar Hunter has an 80.6% chance of victory against an unpromoted barbarian Warrior in a Forest; with 2 experience from Apprenticeship used to purchase Woodsman I, the odds of victory increase to 97.3%. The initial production cost of building the Hunting Lodge and producing the first Hunter is steep, but your Hunters will quickly pay for themselves. This is one of the reasons I favor God King over City States; the +50%

will reduce the sting of the high production investment needed to field Hunters. Of course with God King you will need to be much more careful about the rate at which you expand and be more selective about where (ie how far from your Capital) you found your cities.
Markets: You were right to research
Calendar in your situation; being able to develop those two Incense tiles was an excellent economic boost, and the extra

from the Banana doesn't hurt either. However, since you took this detour, you should probably have also researched
Festivals.
Festivals is a very inexpensive tech with big benefits. The Market is arguably the most important building in the game. The

penalty is outweighed by the

bonus unless your economy is already running at 100% research. For example, in your current situation, adding a Market to each of your cities drops you from 27 to 22

and increases your income from +5 to +20

/ turn. Increasing the research slider from 50% to 80% gives +4

/ turn and 38

- meaning that having a Market in each city would effectively cost you 1

/ turn and give you +11

. Adding Markets decreased the time left to research
Archery from 9 turns to 6.
Another added benefit to a
Festivals detour is the Carnival building. It provides +1

, which would be particularly helpful to you because of the few +

resources to which you have access.
Brakkah: You are right to want to secure access to +

resources, but I feel that building this city was a mistake. Settling deep in the Jungle before you have access to
Bronze Working is almost always a terrible idea. From your current situation you are at least 46 turns from researching
Bronze Working (but probably more, since you would want to finish
Archery and also there are other more pressing techs you should consider researching first). Brakkah is effectively giving you +1

, but costing you 2

in increased maintenance. It isn't growing, and is unlikely to improve at all in the next 70+ turns. You should have settled 3NE of Idris, or possibly 1NW3N of Nameless Tower. Once your area is saturated with potentially productive cities then you should wait until you have
Bronze Working before expanding into the Jungle to the south.
Dianchete (Great Bard): I see that you have a Great Bard, and also that you have not researched
Drama (and so did not get it by being the first to research
Drama) and also that you have no ability to assign Bard specialists (and so did not get it from

points), and so conclude that you experienced the "harpy" event, in which you are given the option to receive a free Great Bard in return for suffering unhappiness in one city for a number of turns. Assuming I am correct, this is likely the single greatest reason for your current situation (ie being so far behind the other civs). The economic and developmental damage done by taking the free Great Bard from this event early in the game can be crippling. Unless the event triggers in a city that is effectively worthless anyway (ie like Brakkah as it is now), or in a city with a great deal of excess

, it is best not to take the Great Bard. Even if you use it immediately to good effect it can be difficult to see a positive return - but in your situation the damage is continually mounting because it is providing you with no benefit and is in fact costing you 1

per turn in unit support.