Short answer - no, you don't have to worry about it.
Long answer is: Methanol exists in (I think) any brewing process. The reason there was poisoning in the bad old days of prohibition is that it has a lower boiling point than ethanol, so when it was distilled, methanol came out first so when some moonshiner was distilling, the initial liquid that was recovered had high methanol concentrations. If that was sold, it was poison.
On top of that, our good old Federal Government INTENTIONALLY poisoned alcohol to dissuade people from purchasing the illegal drug. Yes, out dear old government intentionally poisoned the illegal hooch supply. At least 100,000 are estimated to have died from that.
Moonshiners were brewing hundreds of gallons at a time, and when they distilled (with heat), methanol had a lower boiling point, so that came out first. If THAT was drank, well, quite dangerous.
The rest of the distillation was ethanol (mostly) and water and dilute amounts of methanol.
You will always produce some level of methanol in home brewing, but it's negligible. Beers you buy from a store contain some level of methanol, so do wines. Distilled products (probably) take some care to remove it - although I have my doubts with the cheaper rums..
It's only with distilling when you are concentrating it you have to worry. Distillation is illegal without a license, and you better darn well know what you're doing in order to do it safely because you're vaporizing a flammable gas.
With freeze "distillation", you're just concentrating anything that isn't water. I don't recommend you do this regardless - brew a cider, it's pretty simple, you need to add sugar (white sugar CAN be used, but mix it up a bit), and use a cider yeast. That's quite drinkable. If you do not add sugar, it will be about 5-6% ABV, with sugar, you can get it up to 12%-16%. I'd suggest "brown sugar" - which is really just white sugar plus a bit of molassis.
If you just want alcohol, I guess white sugar + yeast + 1 month + and freezing it will do but you better find a mixer which kind of destroys the point of distilling it.
Look up AppleJack, that's easy enough to make. Trust me, I've made it, and I'm a freaking idiot. You can screw up anything, but brewing cider is one of the easiest things to do. It won't be carbonated, and if you're making AppleJack it certainly won't be carbonated.
Carbonation requires a bit of calculation, and if you want sweet cider that is carbonated, it requires calculation, time, and a way to kill the yeast at the right time. Some people just brew cider wine, add additional sweetener, and then artificially carbonate it. Other people go through all the math of how much CO2 will be produced by how much sugar - but be cautious with this, you're making a bomb if you screw up your calculations - if you want to carbonate, at least for the first time, put it in a box to ferment, and put that box in a box, and do it in a plastic bottle, not glass. Old soda bottle is a bit ghetto but will work, and you can check to see how much pressure it is under.
Soda bottles are designed to handle 90PSI at least. If you buy a coke, and shake it up, it DOES NOT increase the pressure of the bottle. It's at equilibrium to begin with. The tightness of the bottle will give you a good idea of how tight it should be before you pasteurize it - this is usually done by immersing it 140F water until it reaches 140F. That will kill the yeast, but be damned certain you kill the yeast, otherwise, again, you have a bomb.