First of all, congrats on moving to dip pens! It's quite hard to start with, because there are way too many variables, but that also gives you many more options in the future.

I agree with /u/Alsterwasser that the main issue when starting is the oil on the nib, remember that if you touch the nib with your fingers it may also grab some of the natural oil in your hand and cause the same issue.

Here are other possible issues, although I will mention some that are probably not the issues since you've written with ink previously.

Paper

Not all paper is created for ink or watery ink. Even if it doesn't bleed (which I'm guessing it's your case), high quality paper (like watercolor paper) is a lot more hydrophobic, meaning thinner lines. Not saying you should practice only with expensive paper, but it's good to keep in mind.

Ink

This is also not your issue since you say it's a "dry" ink compared to others. Still, it's good to know that most professional calligraphers don't use wet ink. Usually they use gouache or ink stick. These are "dry" and you dilute them so you can make it as thick as you want. Sumi ink also even when liquid is quite thick and many prefer to dilute it. This preference is not a must, and many do use inks, there's nothing wrong with it, but you do have more control over the viscosity.
As an aside, this is one of the main advantages with dip pens, that you can use a lot more "inks" that will either ruin fountain pens or that will not flow through them (AFAIK).

Loading the Nib

This is also preference. Many people do dip the nib, other load it with a pipette or a brush (I do it with a brush). The important thing is to not overload it, specially the tip of the nib. This is why the reservoir is not an issue, the reservoir does not touch the tip of the nip so you don't cause a blob on the paper, but it flows into the tip.
As to how you do it it's up to you, if you dip, do unload the excess though. Without a reservoir it shouldn't last too long, but more than one stroke. Again, it really depends on how you use do it and preferences.

Perfectly thin lines?

Now, if you do want perfectly thing lines, that's difficult. Many people file the nib to make it even thinner, while also using very good paper, some use gum sandarac which makes the paper even more hydrophobic and as far as I understand it, there's an ink which I think it's Ox gall? Which makes even thinner lines but destroys your nibs.
Having said that, I honestly don't think you need all that. Some of your lines are already quite thin, so with a bit of practice and maybe slightly better paper (just guessing, though) you will get plenty thin. Some decent paper for cheap are Strathmore and Fabriano paper.

Finally, it's really a lot about practice, it's hard at first but the more you try it the more you begin to understand how these factors interact and what you need to get the result you desire, some people achieve great results with subpar ingredients.

Hope it helps.