yes-  EtBr does intercalate very effectively in dsDNA - now if you denature the same DNA to ssDNA - the bases dont necessarily form a perfect duplex. however to protect its hydrophobic bases from the water around, it does attain arbitrary sec structures by non specific pairing. Those non specific hydrophobic cores are enough to trap EtBr and increase its fluorescent yield which one will see as fluroescence. However, one must note - that the EtBr binding is going to be quantitatively SIGNIFICANTLY lesser to ssDNA of the same size and concentration as that of a corresponding dsDNA. Having said all this - I must add that EtBr fluor/binding to ssDNA is not quantitative and varies depending on gel conditions. The fluctuation is much lesser for regular dsDNA. 

Hope this explains

You can use Alkaline agarose gels to observe single stranded DNA.

Alkaline agarose gels are run at a pH that is sufficiently high  to denature double-stranded DNA. The denatured DNA is maintained  in a single-stranded state and migrates through the alkaline  gel as a function of its size.

Method

1. Prepare the agarose solution by adding the appropriate amount of powdered agarose to a measured quantity of H2O in an Erlenmeyer flask or a glass bottle.

2. Loosely plug the neck of the Erlenmeyer flask with Kimwipes. When using a glass bottle, make sure that the cap is loose. Heat the slurry in a boiling-water bath or a microwave oven until the agarose dissolves.

Heat the slurry for the minimum time required to allow all of the grains of agarose to dissolve. Check that the volume of the solution has not been decreased by evaporation during boiling; replenish with H2O if necessary.

3. Cool the clear solution to 55'C. Add 0.1 volume of 10x alkaline agarose gel electrophoresis buffer, and immediately pour the gel.After the gel is completely set, mount it in the electrophoresis tank and add freshly made 1x alkaline electrophoresis buffer until the gel is just covered.

Do not add ethidium bromide because the dye will not bind to DNA at high pH. The addition of NaOH to a hot agarose solution causes hydrolysis of the polysaccharide. For this reason, the agarose is first melted in H2O and then made alkaline by the addition of NaOH just before the gel is poured.

4. Collect the DNA samples by standard precipitation with ethanol. Dissolve the damp precipitates of DNA in 10-20 µl of 1x gel buffer. Add 0.2 volume of 6x alkaline gel-loading buffer.

5. Load the DNA samples dissolved in 6x alkaline gel-loading buffer into the wells of the gel. Start the electrophoresis at

Hi. Ethidium Bromide is not useful for visualization of single strand DNA because it sticks between two strands. There are many dyes for staining and visualizing single strand DNA like SYBER GREEN, SYBER GOLD, GEL STAR, Diamond Nucleic Acid Dye and so on. See this link

http://biotech.about.com/od/buffersandmedia/tp/DNAStains.htm

yes-  EtBr does intercalate very effectively in dsDNA - now if you denature the same DNA to ssDNA - the bases dont necessarily form a perfect duplex. however to protect its hydrophobic bases from the water around, it does attain arbitrary sec structures by non specific pairing. Those non specific hydrophobic cores are enough to trap EtBr and increase its fluorescent yield which one will see as fluroescence. However, one must note - that the EtBr binding is going to be quantitatively SIGNIFICANTLY lesser to ssDNA of the same size and concentration as that of a corresponding dsDNA. Having said all this - I must add that EtBr fluor/binding to ssDNA is not quantitative and varies depending on gel conditions. The fluctuation is much lesser for regular dsDNA. 

Hope this explains