Frequently used words are often just written in Hiragana. That's why one normally writes あります instead of 有ります. And yes, they mean the same thing. When you've read enough Japanese texts, you'll get a good idea to which words this applies. 行く and 来る are single words, and when they get inflected, they stay single words. That's why you write 行きます and 来ます, and not 行来ます (because even though "kimasu" is phonetically a part of "ikimasu", that's just coincidence). However, you can combine two Japanese words into a single compound verb. In that case, you normally use two Kanji, one for each verb, like in 繰り返す. But for very frequent compounds, sometimes you only use the Kanji for the first verb, and write out the second verb in Hiragana. Again, you'll pick this up as you read Japanese texts. To sum up, just knowing all the Kanji readings doesn't allow you to read Japanese texts. You must recognize the words themselves to be able to read them (though often you can guess, even if you don't know the word). So it's not a very logical writing system (which is not so surprising, considering that Chinese characters where meant for Chinese, and not for Japanese. If one would try to write English in Chinese characters, one might end up with a similar system).

[2 answers because of character limit] The general idea about the usage of Kanji is that words imported from Chinese get written as in Chinese (Onyomi, sound-reading), but that words of original Japanese origin use a Kanji that matches the meaning, and then the ending is written in Hiragana so it can be inflected (Kunyomi, meaning-reading). However, there are a few exceptions: Sometimes there's no single Kanji that matches the meaning, then one Japanese word uses several Kanji with a combined meaning. This happens for example with 今日. You just need to learn these as exceptions. Unfortunately, most dictionaries don't indicate these as exceptions; so in my own wordlists I use for learning I've always marked these. In the beginning, I also marked Kunyomi and Onyomi readings, but after a while this is no longer necessary. Sometimes there are several Kanji matching the meaning, so one can use a particular Kanji to express the intended nuance. For example, you can write みる not only as 見る, but also as 看る, 観る, 視る and 診る, each with its own special nuance of "to look, to see". Sometimes a Japanese word is written phonetically using Kanji. So even though it's a Japanese word, the Onyomi reading is used, not the Kunyomi. This is called あてじ, "assigned characters". 寿司 (sushi) is an example. There are some other classes of exceptions, but I won't go into these here.