I tested, separately, acetic and citric acids for cleaning steel parts. After 24 hours I have moderate results for acetic acid, and good results for citric acid. But in both cases, rust doesn't disappear fully.
I have two question:
P.S. I'd like to get clean iron without gray protective coat, like rust remover from auto parts shop.
Long, long time ago I was employed to formulate rust removers for iron. We needed to be concerned with toxicity, corrosivity, cost, waste disposal, effectiveness, speed, damage to the (uncorroded) metal, and flash rusting (rapid rusting once cleaner is rinsed off).
Rust isn't just one chemical compound. It is generally hydrates of $\ce{FeO}$ and $\ce{Fe2O3}$ (and there are a bunch of them, even if you exclude hydroxides).
So, since different acids will have different effects with different chemicals, you won't necessarily be able to find the one magic bullet for any and all types of rust. The stronger the acid, the more metal will be attacked, unless passivation is used (there's two types chemical and electrical). Amines are also often used. Strong acids Hydrochloric, sulfuric, nitric, are all more aggressive than the weaker organic acids. Naval Jelly (which I was involved with) uses phosphoric acid, but as you noted, it coats the steel/iron. These mineral acids can be dangerous and can't just be thrown out when finished.
There are alternatives. One trick is to get the chloride, sulfate, or nitrate into solution by using a compound other than the acid. For instance, adding sodium chloride to a solution of citric acid should make the citric acid more aggressive, and yet, won't change the pH. (One reason for this is that $\ce{FeCl3}$ is more soluble than the iron citrate.)
Some de-icers use nitrate or calcium chloride which may also be effective, and of course some fertilizers use nitrates, too (even some for indoor plants). So, if you'd rather not work with the strong acids (unless you're a careful person, you shouldn't work with them), you could try that approach.
As far as I know, the only other acid commonly used for rust removal is oxalic acid. I think Zud cleanser uses it, if you can find it. It's a poison, so don't be licking your fingers until you've washed them (yes, even assuming you DID wear gloves!). I don't think it is much better than citric acid. In fact, I'd guess it's worse in terms of rust removal.
Nitric acid will probably be difficult to find/buy. Hydrochloric acid is available (last I looked) at Home Depot ect. (Look in cleaning products, drain cleaners, and cement cleaners). Sulfuric acid, too. That is also used as battery acid, but I'm not sure if you can buy that at an auto parts store without the lead in it. Do not buy anything with lead in it! Do not use anything (like old battery acid) with lead (Pb) in it. Do not touch...you get the idea, right? Finally, look at a table of pKa values for the acids.
The only other ions I might fool around with would be iodide and bromide, and maybe fluoride, just for grins and snickers. I've no idea where you'd get them. (some aluminum cleaners (Aluminum Jelly?) have fluorides). Hint: one reason citric acid works pretty well is because the salt it forms is more soluble than something like iron phosphate, so it leaves the surface allowing further attack.
So, effectiveness will depend not only on acid strength, but on iron salt solubility. Ideally, you want to avoid any oxidizing acid (since that will dissolve (oxidize) the metal) but in reality, a bit of metal loss helps get rid of that stubbornly clinging rust.
To answer your first question, no, you would mainly just get dilution of the stronger acid (citric) with the weaker (acetic). If you used a citrus fruit as the source of citric acid, it's important to note that there is a fair bit of variation in acidity from one citrus juice to another. The best bet would be lemon or lime juice, which have among the lowest pKa values (measurement of acidity, lower is more acidic) of the common citrus juices. If you just used something like orange juice, you might notice significant improvement by switching to lemon or lime juice.
Your second question probably is the right way to go. Rust is fairly soluble in dilute solutions of strong acids like hydrochloric acid (the acids you have used so far are weak acids). You can get consumer-grade hydrochloric acid from a number of sources, the best probably being an aquarium or pond shop. These products usually have names like "pH down" or something indicating that they are acidic. What you want to do is look at the ingredients for a product that is just dilute hydrochloric acid, without a bunch of other stuff. Be sure to read and follow all of the precautions on the container, particularly with respect to wearing eye protection.
Another alternative source for dilute hydrochloric acid would be rust-cleaning products from a hardware store. These typically have a detergent of some sort mixed in with the acid, which is OK, and this may actually be your best solution depending on availability where you live.
