re: Veneering Questions

Typically you always want to veneer both sides to prevent your wood from warping.
There are exceptions however. I find that veneering a single side of hardwood with a similar species and grain running the same direction usually works fine.

The condition gets worse with veneering plywood, but having the single layer of veneer with grain running the same direction as the plywood face being covered seems to work "best".

Always seems worth it to do both sides even if you use a different backer species of veneer.

As veneered things get larger, the glue used starts to reveal monsters. Things like creeping and splitting, etc.
For narrow strips like your drawer fronts you are probably going to get good results with just about any adhesive.

For the smaller stuff I do, I really like the plain old TB cold press. Of course regular PVAs and hide glues are also up to the task.
One thing to watch out for is if your veneer has large pores or is a burl. The glue can squeeze through these openings and make a mess.

If you use a dark glue, the lines would be invisible,
One technique is to use plywood and band the edges with walnut. You can miter the banding to hide and end grain looking bits.
Sand flat and veneer.
Small potential of the banding telegraphing through if it expands more/less than the plywood in thickness.

Of course edge banding is a traditional way to hide the substrate as well and you can make some nice beaded details.