From what I’m reading, beer line length and diameter can have a dramatic impact on kegged beer. I’ll really only need a very short distance of beer line as I’m running a picnic faucet setup that is staying inside my freezer. Do I want to go longer for any reason? What about diameter?
Secondly, does the gas line length or diameter matter?
The gas line diameter or length does not matter.
As far as the beer line goes, when I had a cobra faucet that was inside my beer fridge, I used 3/16" ID and ~5’ long. This was at a serving pressure of ~10 pounds at ~40 degrees. Worked fine.
This manual explains it all.
http://www.draughtquality.org/wp-content/uploads/2012/01/DQM_Full_Final.pdf
Going back a few threads, I asked the same question (in a different way). Steve In TX came back with “try these” http://myadventuresinbrewing.blogspot.com/2009/07/too-much-foam.html?m=1.
I did and they work! I put two of these puppies in my keg dip tube from the top. I’ve got 2-1/2’ of 3/16" hose to my picnic tap and the pressure set at 12-14 psi. Perfect pour every time! Caveat: I strain out all hop bits and such putting the wort into the fermenter so there is nothing that can plug up the restrictors.
Hopefully there isn’t a prop 65 warning on those. 
Well played…
You need the pressure drop in the system (keg fittings, tubing, faucet, gravity, etc.) to balance out the head pressure on the keg. For an extremely short line, it would be nice to use 1/8" ID beverage line, but it may not fit on all your fittings. For 3/16" line, you’ll want at least 5 ft (at 10 psi) and probably closer to 10 ft for normal serving pressure.
http://seanterrill.com/2011/11/11/a-more-accurate-approach-to-draft-system-balancing/
From Micro-Matic Advanced Draft Training:
Temperature is the 1st determining factor for everything else in a draught system.
For every degree above 380F, the internal keg pressure increases 1/2 lb as the CO2 expands.
380F is the most stable temperature for CO2
At 380F, most kegged beer requires 12-14 lbs. of internal keg pressure in order to keep the CO2 balanced within the beer.
With very short lines it’s gonna be difficult to get enough restriction applied to the keg while also keeping your flow rate low enough that beer doesn’t come flying out of your faucet… resulting in a ton of foam 
The ideal flow rate should be 2 oz’s/ sec. The best way to test this is to hook up a cleaner pot full of water to your system and pour into measuring pitcher. i.e. start stopwatch as soon as you open the valve and stop at 15. You should have 30 oz.'s of water in your pitcher.
To adjust the flow rate while keeping the keg pressure ideal, you can utilize different diameter tubing. Tubing diameter is measured by the “I.D.” (interior diameter). I’m assuming you’ll be using Vinyl so I’ll list the restriction measurements for each size.
3/16" - 3 lbs/ft
1/4" - 0.85 lbs/ft
5/16" - 0.40 lbs/ft
3/8" - 0.20 lbs/ft
1/2" - 0.025 lbs/ft
To sum everything up in an easy way, if you use 3/8" hose with a length of 6’, you won’t have a problem giving your beer the CO2 it requires while still providing enough restriction to keep your flow rate to 2 oz’s/ sec. Since 3/8" hose is so standard you’ll never have to retro-fit anything to your system.
Oh yeah! Most people use strait CO2 in their systems - which is perfect… as long as you’re running through more than a keg per week - however, CO2 will start to dissolve into the beer after about 3 days, resulting in added carbonation and eventually your beer becoming pure foam. If you keep your beer longer than this, you’ll want to use a “mixed-gas” blend, which is normally CO2 mixed with N2 which will allow you to maintain the proper applied pressure while reducing the likeliness that you’ll over-carbonate your beer.
I wish I knew this prior to getting a keg setup! There is no way I will go through beer that quickly. Is that a hard and fast rule?
Is this normally available at places that sell CO2?
The CO2 will eventually equalize to the same pressure in the beer as is shown on the regulator, the beer will not magically absorb a higher pressure than is being applied. It will not turn to all foam if you don’t drink it in a week, I have beers on tap for a couple months that are still pour great.
Ignore that 3 day note. That is geared towards bars with long runs where they need to use excessive pressure to push their beer. Beer gas is used for long runs as the nitrogen doesn’t dissolve easily into the beer. This allows the bar to push the beer with more pressure without the fear of over carbonating the beer.
+1. I keep kegs on for months sometimes, too - at the pressure I want. I call BS.
Did you mean to say 38F?
Just checking because 380F looks just a little bit high.