Minecraft – Thaumometer on bed

If you're willing to carry a door on you, the quickest shelter you can throw up is to just dig a 1x2 hole into the side of any hill and throw down a door to seal it off.

If you don't have a door I suggest the following:

  ▓▓▓ ▓▓▓
    ▓▒▓   top down view 
    ▓▒▓   
    ▓▒▓▓  ▓ 2 rocks
    ▓▒•▓  ▒ 1 rock
    ▓▓▓▓  •   you

The key thing here is that by being off to the side you aren't in range of arrows, but you still maintain a path to light so you can see the sun up (you can also listen for music, but I often disable sound). You close off the entrance with single rocks so you leave a 1x1 path which zombies can't come down.

What you should do is make the water only one block deep, so that it all levels out. See the question that ZoogieZork posted. After that, you can dig as deep as you want and the currents shouldn't appear.

In general, here is a good technique for building rivers (top-down view):

█▒█▒█▒█▒█▒█▒█▒█... | █ = block
.█▒█▒█▒█▒█▒█▒█▒█.. | ▒ = water source
..█▒█▒█▒█▒█▒█▒█▒█. | . = empty block

First, you want to dig out a path for your river. Place alternating blocks and water sources along where your river is dug out so it looks like a checkerboard. Then, destroy all the blocks. Because there are water sources every other block, the space created by the blocks being destroyed will turn into source blocks themselves and create a nice and smooth river.

In your case, you would probably be able to build this pattern right up to one block before the lake. When you've destroyed all the blocks and the river is nice and smooth, you should be able to connect the lake and the river and the connection between them should level out.