Interesting question. I have three or so answers; I feel like my answer to kernel of corn is a bit weaker than that of wheat berry, but I guess you can be the judge of that.
Kernel of corn
Superstructures
The modern appearance of what we Americans know as corn (maize) is deceiving as to its history. As you may or may not know, maize is not a natural plant, and could not survive in the wild by itself -- it was originally domesticated by pre-Columbian Americans over the period of a 1000 or so years from its natural ancestor teosinte. It cannot reproduce in the wild, primarily because it has no good vector of reproduction; plants, being sessile creatures, and being intensely competitive for space, often have to adopt "natural" vectors to transport their seeds from their birthplace far and wide so their progeny have the best chance to survive. Most fruits, sugary and pleasant smelling, have adopted animals as their vector to transport their seeds; teosinte, and other grains of the grass family, adapted to drier, more arid locales, adopted wind as their method of seed dispersal.
Now, the first thing one has to do when domesticating a plant to perform human bidding is to isolate it from its wild brethren, so that they don't transmit their unwanted genes into the domesticate. Or, said another way, the pro-Columbian Americans who domesticated maize had to eliminate the dispersive abilities of teosinte, in order to select for bigger seeds that give maize is nutritive value. That in turn, meant they had to reduce or eliminate the superstructures of the teosinte seed that allowed it to better disperse and survive. I.e., domestication entailed the reduction of the protective seed coat that enveloped the fruit, to offer it less protection from the elements; and the strengthening of the rachis, normally brittle, that attaches the individual fruits attached to the cob. Well, OK, you say -- why does all this matter? The below image will make the point clearer.
Figure A is "modern" corn. Figure B is completely wild teosinte, and Figure C is teosinte with a maize gene introgressed into it. Figures G and H are maize with various teosinte genes introgressed into them. Do they make the kernel nature of maize clearer?
What I'm trying to show by including the above image is that during the time when western Europeans would have been introduced to maize, maize looked intermediate from what it looks like in Figure A and what it once looked like as wild teosinte in Figure B. Understandbly, the pre-Columbian Americans didn't understand genetics, didn't have modern breeding practices, and didn't have the techniques of The Green Revolution to perfect their staple. Humans have since engineered modern maize to be basically "all seed" and "no protection", but in the time of the pre-Columbian Americans, the seedcoat of fruit would have been much more apparent, and the rachis would have been thicker, like that of figure B's. The kernel nature of maize at the time would have been much more apparent.
Native Americans popped corn too
Being a member of the grass family, and adapted to arid environments, teosinte (and hence maize) seeds harden quickly once liberated from the stalk so as not give up excess moisture. The first teosinte seeds pre-Columbian Americans experimented with would scarcely have been edible. As a result, some archaeologists and anthropologists think, and have demonstrated in the lab, that the first Americans who set about domesticating teosinte originally popped its seeds to extract their nutritive value. If popcorn, and the inevitable hardened seeds associated with its making, were served to the first Westerners to experience maize, the kernel nature of the staple would also have immediately suggested itself.
Wheat berries
Phew! On to your second question.
According to Merriam-Webster's Collegiate Dictionary, p. 1424, a wheat berry is an "unprocessed whole kernel of wheat", and as a term it has been attested since 1848.
At first glance, viewed solely botanically, the name wheat berry is kind of puzzling, for the reasons you mention. But the problem is solved when one realizes that ordinary berries and wheat berries serve the same functional role in two immediately recognizable activities: regular berries dye clothes for the tailor, and wheat berries dye bread for the miller, when ground into flour as middlings. I quote from The Technics of Flour Milling: A Handbook for Millers (1904):
In dealing with wheats it is usually the custom to look
at them from a point of view characteristic of some property
which the sample under observation is mored noted for. For instance,
English varieties are relied upon for colour and flavour
more than strength, and in like manner many kinds of Russian samles
for strength, without special regard to their qualities which they may or may
not possess to any extent....the point to be here noted is this —
that the two principal essentials are strength and colour...
In fact, this "berry"-like nature of grains was noted long before wheat berry came into its own. From The Encyclopedia Britannica, Volume 12:
The word "grains" was early used, also in French,
of the small seed-like insects supposedly formerly to be of the berries
of trees, from which a scarlet dye was extracted (see COCHINEAL
and KERMES). From the Fr. en graine, literally in dye,
comes the French verb engrainer, Eng. "engrain" or "ingrain", meaning
to dye any fast colour.
In other words, the "berry"-like nature of some grains is where we get our verb ingrain -- meaning to impart some essential quality internally, like which does dye -- from! So in fact the name makes perfect sense.
Avoid biweekly altogether. Use fortnightly for "once every two weeks", and twice a week for, well, "twice a week".
Not everything has to be a single word, so don't be afraid to use more than one word when you want to use clear, understandable, unambiguous language.
If they have problems with fortnightly, use every other week, or let them into a little secret: fortnight comes from "fourteen nights", or two weeks.
Edit: From the comments it's clear many Americans won't understand or are uncomfortable with fortnight so, to be safe, use the aforementioned every other week.
Best Answer
How about "Optician's?"