I haven't checked your math in detail. The total cost of recipes, energy, and crafting fees could be right. For experienced players you should definitely ignore the cost of fire crystals below 5-star. For really experienced players you should also ignore the cost of orbs, especially 5-star ones. So crafting ends up being much, much cheaper than the Supply Depot.

To answer your question, I'll mention Fehzor's standard advice: Radiants and crowns are the real bottleneck, so you should focus on farming them. While you are doing that, you will find enough orbs and other fire crystals.

For your specific case, it seems you are working towards getting past the 5* hall of heroes mission.
In this case, you already have 4 4* pieces of gear that you can upgrade.
Logistically, if you want the 5* version of those items, it is cheaper to craft them up than it is to buy the 5* from the supply depot.

If you wanted one from a different crafting line, it will either cost in time or resources. Both are relatively reasonable options at your point in the game.
As Bopp pointed out, crafting is significantly cheaper for veteran players because we have plenty of fire crystals to cut up the cost associated with crafting.

The majority of items require heating and unique variants to function. A good example of this would be something like ash of agni-

Ash of agni (5*, level 1, no UV) requires +6 ctr to get to max, or both armor pieces and a trinket. = not feasible
VS
Ash of agni (5*, level 10, CTR: Very high) is ready to go without any gear restrictions, trinkets, etc. = over powered

The bulk of the cost lies in getting these two things, radiant fire crystals and unique variants that don't suck, so you really can't afford to budget the 3.5K CE towards crafting costs. Instead, you would want to focus on finding elite/advanced orbs of alchemy when you're new and then transition into farming dreams and nightmares for radiant fire crystals as soon as possible.

This transition is not an easy one and really comes down to just flat out "getting good". During this "getting good" period you're likely to find all of the eternal orbs and shining fire crystals that you will ever need.

Nitesta, your comments have devolved into "Where can I find orbs of alchemy?" That is a frequently asked question. My prepared answer, including links to data sets and guides, is here. The short answer is: Farm crowns and buy orbs with crowns.

You know that you get some orbs by playing the missions too, right? You can get up to the 4-star level without much grinding.

I can't help you much on Auction House stuff, because most of what I knew no longer applies. But for starters you can re-sell recipes that are available only at Basil. These are mostly boss item upgrades, but be careful, because some of those don't sell well. For more information, you might search Google (not the forum's built-in search) for something like "auction house guide site:forums.spiralknights.com".

Your weapons are fine. But don't use exclusively elemental weapons. In most areas of the Clockworks you want two damage types, not one. Your shield is terrible. For more advice, try the armor section of my detailed sword guide.

Even as a Tier 3 Knight, I usually make money through T2 runs. Start at Moorcroft, grab some recipes, and then finish by going through the Royal Jelly Palace or the Ironclaw Munitions Factory. 3* recipes are one of the best investments of the game. If you get the right ones, you can reliably double, if not triple your investment.

Off the top of my head, these are the most profitable...

Dark Chaingun
Kilowatt Pulsar
Flaming Pulsar
Freezing Pulsar
Elemental Blaster
Pierce Blaster
Shadow Blaster
Tundrus
Toxic Catalyzer
Twisted Snarble Barb
Twisted Targe
Lightning Capacitor

Some of these reliably sell for ~12,000 crowns. There are others not on this list that can go for between 6,000 and 8,000 on a good day, but usually I don't bother with them.

EDIT**

If you want to play the AH in general, then basically do 2 things. First, buy something that's related to a promo. Ideally not something like the Hallow stuff (which is basically spilling out of everyone's ears at this point), nor should you use things related to repeating events (Apocrea, Tortodrone, Katastrophe). Stuff like Sealed Pauldrons and Spiralhorns are good examples. Second, wait a few months before selling. That's pretty much it. You can take something worth ~30,000 cr during the promo can sell for 80,000 - 100,000 a few months later.

Thanks Flow chart for pointing that thing about 2 star orbs. Thank you Traevelliath for your information. I made the mistake of buying 4 star recipes and now the only way i can think to sell them is bid them to 10k since i've wasted money posting them on AH twice.

Also, Haunted-Soul, what do you mean you couldn't go through all the grinding? What did u end up doing?

Also I want to stay a F2P player.

(this is Nitesta btw. This is my alt)

Sounds like you're having a few problems.

A) You're having trouble finding orbs of alchemy.
B) You're having trouble in tier 3 of the clockworks.
C) You need more crowns.

There's different solutions to each - orbs of alchemy are rare drops and if you're trying to get them it's best to farm for crowns for energy to buy them from the depot. If you have too much time and are up for a lot of grinding, then specific levels are great for finding certain orbs. Tier 2 bosses work great for elite orbs of alchemy, and speedrunning the first depth of the mission "Sewer Stash" will often drop elite or advanced orbs. Tier 2 arcade is also a great place to farm for advanced orbs.
Eternal orbs drop in abundance in tier 3. When tier 3 becomes your norm then you'll be drowning in eternal orbs of alchemy and shining fire crystals. As of this post I have 402 eternals and 44,973 shining fire crystals. They just become an endless resource after you finish your first gear set that requires them.

Now, in tier 3 of the clockworks enemies do get a bit more aggressive. If you're having trouble there I would recommend farming tier 2 missions, preferably bosses or arcade gates with arenas (for profit), or levels you have trouble with (candlestick keeps, likely compounds). Once you can reliably beat tier 2 levels on elite difficulty, jump back into tier 3, but start on the "advanced" difficulty. You'll get less drops but once you get the hang of enemies you can pump that up to elite and rake in the delicious rewards!
If advanced is too hard then you can always jump down to normal. If normal is giving you problems then I'd say go back to tier 2 or try to find a few talented party members to tag along with you. Prioritize survival if you have a strong teammate.

Lastly, getting crowns is best achieved via boss strata. You get bonus crowns after getting enough tokens to buy a weapon or armor, which you can then sell to a random Stranger merchant for some extra money. Higher star level = more crowns.
The auction house used to be much more profitable - selling materials had meaning when we all didn't have hundreds of each, and boss recipes were valuable because most players only could go on so many runs a day searching for them. Now a lot of it is UVs and costumes/accessories. If you don't have UVs, costumes, or accessories, then for the most part you're kind of out of luck without some starting funds and hoping to snag items for low prices and sell them at a higher - but still reasonable - price.

I'll come along with ya Nitesta - I need to grind, I so rarely get eternals it's not even funny XD

I don't know, other than: Visit the forums every day, see which threads have been updated, and read the new posts.