Contrary to popular opinion, a starter is not a required piece of equipment for most engines. I've gotten along for years leaving mine at home (I bought it for boats, not planes). Occasionally I need it for starting a particularly stubborn (tight) new engine, such as the K&B 3.5cc that I've been breaking in, but mostly I don't use the starter on airplane engines. Learning what your engine wants in the way of priming will give you quick starts either with or without a starter. I always get a chuckle when I see someone stick a starter on the spinner and crank the engine for 20 or 30 seconds before it starts. Unfortunately, I can only imagine how much wear is being caused spinning the poor thing so long while it's dry.

Every one of my engines is slightly different when it comes to priming. Note, priming is ALWAYS done with the glow driver OFF. When I can get to the carb, I cover it with my finger and flip the prop the appropriate number of times. If I can't get to the carb, I cover the end of the muffler and flip the prop. The pressure in the muffler forces the fuel into the carb. For a new setup, such as a cowled engine where I can't get to the carb, I've found it's helpful to go through several cycles of staring with the cowl off. This lets me see how much priming it takes to get fuel to the carb.

Not sure what you mean by "fine needle", I've usually heard them called high speed and low speed (or perhaps idle). As has been suggested, having a tach is very helpful for setting the high speed needle. I tend to be conservative, I want my engines to last a long time and I don't want deadsticks from the engine running too lean at the end of the flight, so I back off a little more than 3-400 RPMs.

It's hard to diagnose engine tuning problems without being there, but my guess is your problem is a combination of low voltage on your glow starter and your engine being set too rich. I never had much luck hand starting engines with glow starters. Glow plugs are designed to be lit with 1.5 volts. Since the glow starters are powered by a 1.2 volt battery, they are at a disadvantage compared to a 1.5 volt battery, or even better, a power panel with adjustable output (this is what I use). The self contained glow starters seem to work best when used with an electric starter.

Anyway, if you combine low voltage on the glow driver with a slightly flooded engine, you've got a situation where the plug will not be hot enough for the plane to start. This is particularly true when the engine is inverted, the fuel can pool in the glow plug and without enough power, the element stays cool. When you encounter this situation, pull the glow plug out and have a look at it. See if it's wet, and if perhaps fuel comes out of the glow plug hole. If either of these happens, you know it was flooded. Put the plug in the glow starter and see how it does at boiling off the fuel. I know the glow driver in my power panel has no problem with this. Flip the engine over a few times with the plug out to help clear the fuel, put the plug back in and try starting it.

Once you get the engine running, procede quickly to getting the high speed needle set according to the manufacturer's instructions. One trick I've found for getting the low speed needle set is to see what happens when you remove the glow starter while the engine is idling. With the glow starter attached, run the engine to full throttle to clear out the carb. Bring it back down to idle and leave it there for 5-10 seconds to stabilize. If the engine slows and dies with the glow driver on, the idle mix is either way too rich, or more likely, too lean. Watching the exhaust should give you an idea which is true. If the idle is stable with the glow starter on, remove it. If the engine slows and dies, or slows significantly but the engine is able to keep sputtering, I've found that means the idle mixture is too rich. If there is no change when you remove the glow driver, it's either just right, or perhaps a bit too lean. Once you have the idle set so there is little to no difference in RPMs with the glow starter on or off, do the final setting of the low speed needle by testing the transition through midrange to high speed.

One that fits. Sorry for the wise a$# answer. You really can use anything that fits, including left over pushrod material. Note, if you use pushrod material, file a flat spot so the set screw has a place to bite, and so the rod won't come out even if the set screw loosens up a bit.