How to hook up this kitchen drain?
Personally, I would not use flex pipe of any kind on a kitchen sink.  I know there is no "code" for that, but from experience it usually ends up bad.
The ridges of the flex pipe create areas that food or anything put down the kitchen drain can sit and rest and fester.  This will cause clogs and smells much quicker.
You also can't get the P or S shape that is often required by codes out of a flex tube which is designed to prevent sewer gases from coming back up into your kitchen sink (in part).
Also, the flex tube is typically not as strong as a schedule 40 or sometimes even a schedule 20 pipe and may be more prone to bursting.  This is also true for flex pipe depending on the location of the sink in the house (how close it is to an outside wall) and the location of your house in general (north where it gets cold or in the south where its always warmer).  If its near the outside of the house in a colder climate, water that didn't drain properly (which is a constant in flex pipes like that), will freeze and expand and possibly cause the pipe to burst, or atleast weaken and stretch the flex pipe over time.

In general I would not use this flex pipe long term, I know that is not answer you are looking for, but I would only use it as a temporary thing.  Look at getting some schedule 40 pipe for the long term.

As far as fitting that end of the flex hose into the wall drain....that opening is a regular PVC pipe it looks like from the picture.  What I would recomdend doing is getting 2 PVC pieces.  First is a PVC bushing (sometimes listed as just an adapter or reducer depending on size of pipes) with a female thread inside.  This you can find at just about any big box store.  Here is a link to Lowes (first in google search results).  Second is a PVC Adapter that will screw into the bushing/adapter/reducer.  This second one will have ridges on it, and you should be able to push the flex hose on to it and then THIRD use a standard pipe clamp ring to hold it into place.  You might want to glue the FIRST piece to the drain in the wall if this is a fairly permanant setup (less than a year I would say), otherwise don't glue it if you plan to redo it soon.
All together it should only run you about $10 depending on sizes and such.  I wish I could give you more specifics but we would need to know the size of everything.

Regarding the inlet for the drain for the dishwasher.  A plumbing supply store might have the adapter you need.  I would look locally for a plumbing supply store and they will say "oh yeah, its this thing" or "no, you need 5 fittings to go together".  The big box stores won't have something exact, but between a few bushings, adapters and fittings you should be able to make something work.  Again, I don't know the exact sizes of those, so I can't give you exact help with that.  Going to the big box store and having a few fittings to get what you want I would say is the last resort, but if so, bring it in and there is usually an associate that likes the challenge.