What would the specific name for them be? Does anybody know of a website that can give me a list? (Ex. I search for "car", and it gives me "CARpet", "niCARagua", etc.)
Oxymoron is one word. And it means a phrase that contradicts itself (eg, military intelligence).
A [b]simile[/b] is like a metaphor. It's comparing something to something else, but saying they are similar, not the same (hence the name). Eg, "The sun was like a bright hot burny thingy".
Just making sure you know what you're talking about.
Do you mean syllables? I don't think there's a name for a random sequence of letters in a word that happen to form another one. You could invent one, like "subword".
As to your second question, search for an online dictionary that supports wildcard searches. Then you can search for, say, *car*.
an anagram is a word that can be twisted around to make other words/names
like rain and Iran. In order for it to be an anagram, it must use every letter, so no, this would not be an anagram.