Random Puzzles 

Workings

Hint
Start by filling the 11 gallon container.

Answer
Here are the contents of the containers after each stage:
A  B
0  11  fill B
7  4   fill A from B
0  4   empty A
4  0   fill A from B
4  11  fill B
7  8   fill A from B
0  8   empty A
7  1   fill A from B
0  1   empty A
1  0   fill A from B
1  11  fill B
7  5   fill A from B
0  5   empty A
5  0   fill A from B
5  11  fill B
7  9   fill A from B
0  9   empty A

This leaves 9 gallons in container B.

Workings

Hint
Make sure you answer the question asked.

Answer
10,001.

Workings

Hint
Another example, PEN is a complete word because:
   -en = ten
   p-n = pin
   pe- = pea

Answer
Three of the words are not complete: flew, rook, lamp.

Reasoning
The remaining 7 words can be changed as follows:
team:  -eam = beam
 t-am = tram
 te-m = term
 tea- = tear

cost:  -ost = host
 c-st = cast
 co-t = coat
 cos- = cosy

flew:  -lew = blew
 f-ew = ---- X
 fl-w = flow
 fle- = flex

ward:  -ard = card
 w-rd = word
 wa-d = wand
 war- = warm

fail:  -ail = nail
 f-il = foil
 fa-l = fall
 fai- = fair

rook:  -ook = book
 r-ok = ---- X
 ro-k = rock
 roo- = roof

soft:  -oft = loft
 s-ft = sift
 so-t = sort
 sof- = sofa

most:  -ost = cost
 m-st = mast
 mo-t = moat
 mos- = moss

lamp:  -amp = damp
 l-mp = lump
 la-p = ---- X
 lam- = lamb
Note that LARP is an uppercase acronym, and not in any of my word lists.

load:  -oad = road
 l-ad = lead
 lo-d = loud
 loa- = loaf

Workings

Hint
Think of chickens.

Answer
Don't count your chickens until they're hatched.