Newbie questions

I have a cottage that I am going to put a water tank underneath and would like to know if I have the right idea of how things will go together.
This is the order of the water hookup as far as I can see, tank>pump>softener>rust>filter>1 line to water heater and 1 cold line.
I plan to run the pipes inside the cabin instead of the crawlspace to avoid freezing. The tank, pump etc. will be under the kitchen, do I have 1 cold line and 1 hot line running to the kitchen, washer, and bathroom and just T off of the 1 line to the outlets that I need?

That would be pump>pressure tank>filter but it probably isn't needed; unless the water is visibly dirty>softener.

Crawl spaces usually don't freeze as long as you stop air drafts but... how are you planing to prevent freezing of the pump and water in the tank? And why not do the same for the softener?

I am going to dig out the crawlspace big enough to hold all my equipment. I will pour a floor and frame in and insulate the room that will hold the furnace, water tank, softener, pump etc. The rest of the crawlspace will be insulated and some of the ductwork for the furnace will run through the crawlspace but the bathroom and laundry area is at the other end of the cabin from where the water tank is, plus I live in Canada and just a week ago we had -50 temps so just to be safe I am still running as much of the pipes inside that I can. I am planning on putting some crown moldings near the ceiling and hiding the pipes in there. My main question is do I just T off the 1 cold and hot line for all my fixtures or run separate lines from a manifold?

Are you going to use copper or something like PEX? PEX won't be damaged if it does freeze, but the fittings are not immune to damage. If pex, then home runs from a manifold are reasonable. You could do that with copper, but with the cost of materials, it's not too cost efficient. It's a good idea to gradually step down supply line size as you branch off to the various things along the line. How many fixtures are you planning (i.e., how many sinks, toilets, tubs, showers, WM, etc.)? That will help decide the size of the piping needed, regardless of the material used. You can run pex like you would copper if you wish, but home runs have advantages - the fittings can be a big part of the costs, and avoiding them also avoids a potential leak/failure. Note, depending, some people have reported that rodents like to chew on pex, so in a cabin, unless enclosed well, that might be a consideration.

I plan on using 3/4 inch PEX pipe but I don't know what a home run is. If you could explain that and where the stepping down in size would come in I might have a better idea. I will have the kitchen above the area that holds the tank/pump etc. It will have 1 sink and a dishwasher and the washing machine.
Then the bathroom is beside it with 1 sink, toilet and a shower. Should I put a manifold roughly in the middle of the 2 rooms in the crawlspace?

There are numerous ways to do this. You could have one manifold near the main supply line. Then, run to each fixture or run a large line to the area of multiple points of use, then branch out with a manifold there. The home-run is basically, a direct line from the manifold to the point of use with no fittings or junctions in between. A manifold is often the point where you go from one size to the smaller one to output to the fixture.