1) I would guess this is just to make sure that the NaHCO3 dissolves. It should be soluble in water anyway, but if your water is a little basic then the solubility might go down a bit. This step does seem a little odd though.
2) Not sure about this one either, but usually you use cold solutions to either slow down a reaction (in this case an acid/base neutralization) or to lower solubility. Either of these may be the case here. I think it's more likely the latter, since you want to minimize the amount of material that goes into the NaHCO3 solution so you can get all of it out in the NaOH extractions.
3) Emulsification is a funny thing. It tends to happen when you have a solution of some material that has a functional group that is highly soluble in aqueous media and another that is highly soluble in organic media. In this case, an aromatic ring (organic soluble, aqueous insoluble) and a deprotonated carboxylic acid (aqueous soluble, not very organic soluble). So these two functional groups are competing to find the most stable way for them to dissolve. The carboxylate end sticks to the water, the aromatic end sticks to the pet. ether. These attractions make a crude mixture of the two solvents: an emulsion. (BTW, this is a pretty bad explaination. I'm sure you can find a better one)
4) Be aware of the subtle difference between "washing" and "extracting." Washing is treating something that is in one phase (say it's the organic phase) with a solution of some reagent in another phase (e.g. aqueous ammonium chloride soln.) to effect some change on the molecules in the phase that is being washed. In this case the "washing" layer is discarded as the desired material never moves from one phase to the other (the aqueous phase in my example would be discarded). Extracting is adding a solvent (say, ether) in a different phase from solution you are going to extract from (say, some aqueous solution of an organic molecule). The extracting fractions take advantage of the fact that the molecule you want is more soluble in the phase you are extracting with than in the phase you are extracting from. You save the extracting phase (ether) is saved and usually combined after a few extractions. Once the extractions are complete, the phase that was extraced from is discarded (aqueous phase, in my example). Don't dispose of anything until you are convinced that you have all of your material in your extracts!
5) The acidification is to change the solubility of the salicylic acid. Recall that it becomes soluble in water because it is deprotonated. The HCl re-protonates the salicylic acid so that it is again more soluble in organic media than in aqueous media. Then you can extract it into chloroform.