Q 1: what material (MDF, or pine laminated pieces)

Pine is fine... why not solid pine? It's probably cheaper

2: what thicknesses of material (Its gotta be ½", 5/8", 11/16", or ¾",
nom. or not)

1/2 or 5/8 looks nicest, but this is purely utility and you don't have a
planer, so I would go with over the counter 3/4".

3: what joints for front and rear (dovetail, rabbet and dado, lock or
bit)

Dado is quick and adequate for the back. It's not a high-stress joint.
Don't overthink this.

4: what material and thickness for the bottom (white(hard)board,
plywood
or other)

Ply all the way. 1/4 luan is fine for all but the drawers for seriously
heavy items (large quantities of nails, paint cans, *full* case of beer).
3/8 would do there.

Glue the bottom in a dado on all 4 sides.

5: max. Drawer width

Huh? You spec the drawes below.

Joints: I am willing to choose through dovetails by hand for the front and
spend on a hand dovetail saw and guide
http://www.leevalley.com/wood/page.aspx?c=2&p=41718&cat=1,42884. For the
rear join I have been thinking rabbet and dado.

If you really want to learn handcut dovetails, buy the LV sliding bevel, a
square and lean to cut to the line. This is the perfect project to practice
on. The siding bevel is a really nice tool. Not trying to be snobby but I
conside the afforementioned guide to be a crutch. I also am not too fond of
one-trick ponies.

11/16" solid laminated pine ain't bad, but I think I'd prefer to hear that
I
can cut a solid dovetail out of ½" or 5/8" nom. mdf by hand for the front,
and use a really fast machined joint, like a rabbet and dado, in the rear.

The dovetail joint was invented to work well with solid wood (which is very
strong in one dimension be very weak in the other). DT's in MDF is a waste
of time. It has very different properties.


I understand a lock joint can be weak. I may have 4 gallons of paint in
these drawers on rollers. Is there any other type of router bit that can
create a quick strong joint?


Dado is fine for the back
Material: I can use that 11/16" solid pine sideways-laminated that comes
..... Are they
biscuited? Are they lasting?

No and yes in that order. Just glue, which is *stronger* than wood.

What about mdf? Can you cut a dovetail out of mdf?

No No NO.

How does a lock joint
work in mdf?

Probably OK to poor

How does a rabbet and dado work in mdf?

Pretty well

How is mdf for drawers?

Too heavy. Considerably less strong. MDF is flat and cheap. It makes pretty
good counter substrate. It has good compressive strength. However, it is
probably twice the weight/vol of pine and had considerably less tensile
strength.
If it cones in contact with water is will turn to oatmeal in short order.
Did I mention that it's ugly? ;-)

Thickness: Solid pine laminate only comes in 11/16" (actually not sure if
nominal). Should I be complaining it is too thick. Its not a full .750".
But
mdf comes in ½", and 5/8" nominal. That seems a better thickness than ¾",
or
even 11/16", no?

No big deal... the only potential gotcha is using trying to use a router bit
to make a dado, but that's a pitfall for all sheet stock. Never assume
nominal thickness.

Bottoms: I know there are lots of thin plywood ( like approx. ¼" or mm):
which is good?

For utility drawer bottoms, any is fine

What kind of core

Core doesn't matter much because stress is mostly on the outer layers.

What about that thin stuff that backs some
furniture. The cheap stuff. (Hard)board? Comes in white, etc?

Ew! Stay away, except for Quick/dirty/cheap applications.

Width: I can't remember why drawers have a limit to width and I don't know
if my plans exceed this. Am I all right? The 21-3/16"w drawers MAY get
split
bottoms front to back for bottom strength, but will they twist or
something?
Was that width rule by wall thickness, or twist; I can't say.

I'm unaware of rules, but IME that size is fine.

I have a 3 h.p. 10" table saw with a 1/8" 36-tooth carbide tipped
combination blade. I do not want to buy a dado or other blade(s) unless
necessary because I may not keep the saw long.

Why, because you want to get out of the sawdust business, or because that
3HP saw is a POS-direct-drive-universal
motor-only-under-start-up-for-an-instant-when-the-15-Amp-110V-breaker-is-abo
ut-to-pop-3HP-saw?