Does 3/4” pex supply enough water for a house

It depends how many things you intend to use at the same time. Water pressure drops the more things you're using at once. I can run two hoses off a 1" line at once, but I lose about 75% of the water pressure.

If you're running only one thing at a time you should be just fine. If you need two it will be iffy, and I doubt you could do three.

Home run system is very good option. 3/4 supply is good for most houses. If you have low pressure with taps on 3/4 may be small. If you have big house with many lavatories and people 3/4 may be small. I think the easiest way to check is put a gauge at your meter. Check pressure with system closed. Open many taps. If pressure goes way down 25 to 50 percent bigger pipe will not help. You might need bigger meter before bigger pipe makes sense.

Not a calculated method, but if that home is yours and you're planning to spend a good few years in it, I would put in the 1" main PEX to water heater and as you go to edge water outlets of the house, convert that 1" to 3/4". The cost of 1" vs 3/4" isn't too drastic and having the extra capacity, especially to the water heater will help with pressure issues. 3/4" post water heater is good, unless you have 8+ hot drops.

If that home is a builder home and used for investment or you're trying to minimize the cost, do the calculation on needed flow and capacity. Most of the time 3/4" is good for smaller homes.

Regarding manifolds, all builders that I've seen do not use main manifolds and just use tee's and split off the main pex. It appears, labor wise, its less work and less cost since the manifold adds a few hundred to the project and creates further runs but you lose the ability to shut off each drop.

You'll get water.

I've dealt with an older house where the main feed was dropped to 1/2" and they got water.

Mind you, I replaced the 1/2" with 1" when I got to working on the water system in that house, and water delivery improved. But it's more a matter of what you're willing to live with, and how well it works, not complete failure to work.

My rule of thumb (for a single family house of "normal" scale) is 1 inch to the house, 3/4 inch at the hot/cold split, 1/2 inch to fixtures. As with most rules of thumb it's not based on bothering to work out the flow rates and pressure drops explicitly, but it works well enough for me. In my case I have 1 inch from the well - if you only have 3/4" to the meter, 1 inch from the meter to the house probably won't make much difference .vs. 3/4.