First of all the information I'm providing is based on my local codes, your local codes my very.

Quick Answer

You will need to feed the lower floor manifolds with 3/4" PEX inlets and 1/2" outlets. No manifold would be required for the upper bathroom as only 1/2" PEX is needed for both the hot and cold, just tee off the 1/2" lines to feed the sink, tub and water closet. All individual fixture runs would be 1/2" as well.

Detailed Answer

Using manifolds and running to each fixture individually is called a homerun system. This can be less labour but may have a higher material cost. It all depends on how far the groups of fixtures are from the manifold. This method is typically used when the pipes are run through the slab.

Depending on the location of the fixtures, you may want to look at a truck and branch system. This is were you would run two mains and branch off to the fixtures as it passes them. The mains would get smaller as the fixtures are taken off.

Water lines are sized so that the velocity within the pipe is kept below a set point. This is to limit the wear and tear on the pipe material. Different materials can handle different velocities at different temperatures. The max velocity for copper and PVC is 5ft/sec for cold and 4ft/sec for hot. PEX pipe can handle a maximum velocity of 8ft/sec for both hot and cold.

Fixture units (FU) are given to typical fixtures. A FU is a design factor that is used to represent the typical requirement of a particular fixture (it is not a flow rate but).

Fixture Units for Private Use Fixtures (no flush valves):

|--------------------------------------------------------|
| Fixture           |    Hot FU  |  Cold FU  |  Combined |
|--------------------------------------------------------|
| Bathroom Group    |      4.50  |     4.50  |      6.00 |
| Bathtub/Shower    |      1.50  |     1.50  |      2.00 |
| Clothes Washer    |      2.25  |     2.25  |      3.00 |
| Dishwasher        |      3.00  |        -  |      3.00 |
| Hose Bib          |         -  |     7.00  |      7.00 |
| Kitchen Sink      |      2.00  |     1.50  |      1.50 |
| Water Closet      |         -  |     3.00  |      3.00 |
| Lavatory          |      0.75  |     0.75  |      1.00 |
|--------------------------------------------------------|

The above table lists the common residential fixtures and their FU. You can see that a bathroom can be considered one group and has a lower FU then the sum of it's parts. This is because they are typically used by one person at a time so it is unlikely that all fixtures will be running at the same time.

Once we have the FUs, we can look up a sizing chart that will tell us the maximum FUs that a pipe of a set size and material can handle while staying below the maximum velocity. You can view these tables in the Domestic Water Sizing Tables (For Small Buildings) section below.

Based on this information, we can size your distribution system as follows for PEX:

|----------------------------------------------------|
| Fixture Group        |      Hot      |    Cold     |
|                      |    FU  Size   |    FU  Size |
|----------------------------------------------------|
| Upstairs Bathroom    |  4.50   1/2   |  4.50   1/2 |
| Downstairs Bathroom  |  4.50   1/2   |  4.50   1/2 |
| Kitchen              |  4.50   1/2   |  1.50   1/2 |
| Half Bathroom        |  0.75   1/2   |  3.75   1/2 |
|----------------------------------------------------|

So you can see that the pipes feeding each group of your fixtures will only need to be 1/2". Each individual fixture would also be 1/2". However, depending on how the groups of fixtures are located relative to each other, you may require 3/4" pipes to feed more then one group. The total FU of your house is 14.25 Hot FU (3/4"), 21.25 Cold FU (1") and 28.00 Combined FU (1"). The Combined FU is used to size the section of pipping from the cold line into the house to the hot water tank. Don't be alarmed that the cold and combined are sized at 1". This is due to the allowance of the hose bib, which our code now calls for 7 FU. This is too high and has been causing issues in large buildings with hose bibs on small decks, in that the lines are oversized and do not properly flow, allowing for growth in the water. Without the hose bib, your cold is only 3/4".

Domestic Water Sizing Tables (For Small Buildings)

1. Minimum pressure available - 60 PSI at property line. (Greater acceptable).
2. Pressure reducing valve set at 60 PSI minimum.
3. Pressure loss for meter (3 PSI), maximum building height 25 ft. (10.82 PSI)
4. Minimum 0.115 PSI for friction loss. If less than 0.115 PSI, system must bp fully engineered by detailed method or there will not be sufficient water to supply the fixture.

Pipe Flow Velocity Table For: Copper & PVC:

|---------------------------------------------|
| Pipe Size | 5ft/sec (cold)  | 4ft/sec (hot) | 
|           |    GPM      FU  |    GPM    FU  | 
|---------------------------------------------|
| 4"        | 186.65     850  | 149.32   600  |
| 3"        | 106.16     400  |  84.93   295  |
| 2-1/2"    |  74.37     245  |  59.50   170  |
| 2"        |  48.23     120  |  38.58    81  |
| 1-1/2"    |  27.72      46  |  22.18    34  |
| 1-1/4"    |  19.59      29  |  15.67    22  |
| 1"        |  12.86      18  |  10.29    14  |
| 3/4"      |   7.54       9  |   6.03   7.5  |
| 1/2"      |   3.64     3.5  |   2.91   2.5  |
|---------------------------------------------|

Pipe Flow Velocity Table For: PEX, PE, PB, CPVC & Ductile Iron:

|-----------------------------------|
| Pipe Size | 8ft/sec (cold & hot)  |
|           |    GPM            FU  |
|-----------------------------------|
| 4"        |    300          1800  |
| 3"        |    170           750  |
| 2-1/2"    |    152           500  |
| 2"        |     78           265  |
| 1-1/2"    |     44           102  |
| 1-1/4"    |     30            54  |
| 1"        |     20            30  |
| 3/4"      |     12            17  |
| 1/2"      |    5.8             7  |
|-----------------------------------|

Yes. In fact, I had to do this exact same thing in a house in MN that had baseboard copper freeze and burst in an attic. I ended up replacing the cooper between the boiler and the baseboards with PEX.

I'd suggest using SharkBite connectors to transition between the copper and PEX. They're designed for that and it's super-easy to install.

As Ecnerwal points out, be sure to use PEX with an Oxygen Barrier.

While doing this, be sure to fully insulate the PEX. PEX can withstand freezing, but it's best to avoid freezing in the first place. If you can move it into conditioned space, that'd be best. If not, wrap it in quality pipe insulation (not the cheap stuff but the ones that self-seal).

The biggest challenge might be finding just the small amount of PEX needed as they are often sold in large rolls. You may want to check with a plumbing supply warehouse to see if they'll sell you a remnant piece.