Just to state this a bit more clearly, there are two basic ways of dealing with this problem, and jz78817 mentions them both.
Option 1: Treat the fuel
One way to deal with problems of fuel congealing, etc. is to deal with the fuel. You take the vegetable oil and treat it with methanol and either potassium hydroxide or sodium hydroxide. It’s a fairly simple process. You just heat it and stir, basically. The glycerin will settle out as either a liquid or a solid (depending on which catalyst you used) and you are left with biodiesel that most diesel vehicles can use without any modification to the vehicle. There are plenty of folks that are doing this now in their back yards (except that they are usually using waste vegetable oil instead of rotting zombie goo) so this is definitely doable with the limited resources that you could expect during your typical zombie apocalypse. Sodium hydroxide can be found in most hardware stores where it is sold as a drain cleaner, and methanol, as you noted, is easy enough to make.
The process for using fat is basically the same, with one additional step. You need to render the fat first, and to do that you just need to heat it up so that it liquifies, but don’t heat it so much that it burns. Once that is done, then you give it the same basic treatment as vegetable oil.
Option 2: Treat the vehicle instead of the fuel
The second way to solve the fuel congealing problem is to deal with the vehicle instead of the fuel. You need two tanks, one for “good” diesel and one for your waste oil (or pig fat, or zombie goo, or whatever) fuel. Heat from the exhaust is routed around the crappy fuel tank, and you need a switch to select between which tank you want to use. You start with the good fuel, which gets the engine started in lower temperatures and all of that. Then, once the exhaust has heated up the goo fuel into something usable, you switch over to the crappy fuel tank. and then you run off of your crappy fuel tank. Before shutting the engine down, you have to remember to switch back to the good fuel and let it run long enough for the good diesel to push all of the crappy stuff out of the fuel lines, fuel filter, etc. If you forget to do this, then the crap fuel will solidify in your fuel lines and then you ain’t goin’ nowhere, which makes it really hard to escape the zombie hoard.
Folks use modified cars now too, so this is also easily doable during your typical zombie apocalypse. One problem that you have is if you switch over to the crap fuel too soon and it’s not hot enough, the fuel tends to clump and doesn’t burn completely inside the engine. This leads to a lot of deposits building up inside the engine which can cause you problems in the long term.
If you are using animal fat (or zombie fat) then you’ll need to render the fat for this method as well. But that’s all you need to do to it. You don’t need to chemically treat it like you do in the conversion to biodiesel above.
Algae
As far as making oil from algae, many plants produce oils, and certain types of algae, like basically pond scum, produce a pretty decent amount of oil. The algae is put into a press and the oil is squeezed out of the algae cells. The oil and water naturally separate, so you can easily draw off the oil at that point. Sometimes chemical solvents are added into the process to make the extraction more efficient. Once that is done, the algae oil is treated the same way you make regular biodiesel. You mix it up with methanol and sodium hydroxide, extract the glycerin, and you’re good to go.
