grammar - Questions about counters

My first question is, are counters always required when counting things? Can't I just slap a number in front of the noun? For example,「いちりんご」for 1 apple?

Secondly, in Lesson 5 of the Japanese For Busy People I textbook, it states this sentence structure, but gave no grammatical explanation for it -

thingをnumeral(or numeral and counter)ください。

Since it gave no explanation, is this a valid sentence structure, like that of XはYです and noun1のnoun2? Can someone explain this sentence structure to me? Why is the numeral(or numeral and counter) after the particle を? If it is part of the thing, why is it not on the other side?

If you can answer in order and provide any follow-up links, that'd be great! Also, I've only been studying Japanese for almost 2 months, so please forgive all my questions :)

Answer

1. The following Wikipedia article on Japanese counter word explains well about how the counter words or counters (josūshi 助数詞) work in Japanese.

In Japanese, as in Chinese and Korean, numerals cannot quantify nouns by themselves (except, in certain cases, for the numbers from one to ten; see below). For example, to express the idea "two dogs" in Japanese one could say 二匹の犬 ni-hiki no inu (literally "two small-animal-count POSSESSIVE dog"), or 犬二匹 inu ni-hiki (literally "dog two small-animal-count"), but just pasting 二 and 犬 together in either order is wrong.

Therefore, you have to use リンゴ一つ or 一つのリンゴ to express one apple.

2. 
   

   "リンゴをください" means "Please give me an apple". This sentence doesn't specify how many applies you want. If you want to specify it, you have to insert the counter between リンゴを and ください as in "リンゴを一つください." which means "Please give me one apple."

   
   

   The link further explains:

   
   

Grammatically, counter words can appear either before or after the noun they count. They generally occur after the noun (following particles), and if used before the noun, they emphasize the quantity; this is a common mistake in English learners of Japanese. For example, to say "[I] drank two bottles of beer", the order is ビールを二本飲んだ bīru o nihon nonda (lit. "beer OBJECT two-long-thin-count drank"). In contrast, 二本のビールを飲んだ nihon no bīru o nonda (lit. "two-long-thin-count POSSESSIVE beer OBJECT drank") would only be appropriate when emphasizing the number as in responding with "[I] drank two bottles of beer" to "How many beers did you drink?".