[LearnAmazingJapanese]

Hate to throw mud into the mix at the point where it looks like things are getting resolved, but...

What MMM said about "and" is correct:

noun "to" noun = noun "and" noun, talking about those two nouns particularly

noun "ya" noun = noun "and" noun, when those two nouns come in no preferred order, and there might be more nouns in the list that aren't mentioned

When you're talking red and yellow (adjectives, in this case "true" adjectives in Japanese) the "and" that you use is a matter of context:

I like red and yellow = aka to kiiro ga suki desu (here "aka" and "kiiro" are actually nouns as is "the color red and the color yellow.")

I like red cars and yellow cars = akai kuruma to kiiroi kuruma ga suki desu (adj + noun + "to")

In any of these sentences, replace "to" with "ya" to get the same literal translation; but, the implication is that there is more to the list than what you have said.

NOW, at the risk of confusing the issue, in spoken Japanese, rather than "ya," you'll see the word "toka" used quite frequently:

I have to buy some onions and carrots = Tamanegi toka ninjin wo kawanakya ikenai ("toka" means "and," but like "ya" indicates there might be more to the list).

As MMM said, the rule for using two true adjectives (ends in the -i sound) in a row is to lop off the -i from the first one, add -kute, and then stick on the second one:

akakute, ookii + noun = red and large noun
or
osokute, noroma na + noun = slow, dimwitted noun
(here, it's a true adjective first, and then what's called a quasi-adjective, which basically is an adjective that doesn't end in an -i sound).

The conjunctive "and" is the and to connect sentences or ideas. You can do that by ending a sentence in Vte form and going on the the next sentence (... , and...), ending a sentence in the V2 form (... and, ...).

"soshite" seems to be used most frequently at the beginning of a sentence, sort of like starting a sentence with an "And" (even though your English teacher wouldn't approve). You can also use "soshite" towards the end of a sentence with a list of nouns:

ringo, banana, painappuru, soshite mango wo kaimasu = I am going to buy apples, bananas, pineapple, and mango.

Last, but probably least, "ken":

兼 is the kanji for the "ken" that was brought up. This is used mainly in titles like "President and CEO" (shachou ken saikou keiei sekininsha), meaning "concurrently" or "and." You don't use this very much, especially at the beginning of your Japanese language quest, so I'd let it drop for now.

Sore ja.