You seem to be reading texts that are above you skill level. You are maximally vague about the type of text you read (your full description of it is, and I quote, “a book” ;-)), but it is simply no fun constantly having to look up words and being hindered in the process by unknown or ill-understood word forms. Unless you are equipped with supernatural patience, this kind of reading will probably lead nowhere.
Solution 1: Start reading simple texts specifically written for beginners. There are lots of those; in fact, most Latin textbooks for schools start with simple texts, use context and pictures to make guessing meanings easier, and then continuously introduce more and more grammar and vocabulary from chapter to chapter. One textbook using this approach that is very popular on the Internet currently is Lingua Latina per se illustrata (or LLPSI for short).
Solution 2: There is a school of thought that says you should memorize Latin morphology – not the rest of the grammar, just those pesky suffixes – before you do anything else, even before starting with a textbook like LLPSI. And specifically that you should do this by taking a lot of paper and writing down all the declension and conjugation tables (also known as “paradigms”) 100 to 200 times. This is known as the “Dowling method” after William C. Dowling, an Amercian professor (though not a classicist or philologist); also recommended by Luke Ranieri (one of the best Latin speakers in the world, so it sure worked for him).
You say that “nouns have lots of declensions,” and what this tells me is that you haven't looked too closely at verbs yet ;-) You will use up a lot of ink if you really want to go through with this, and I wouldn't really recommend it, but it is certainly a good idea to get your head around declensions and conjugations early on, and it is also undoubtedly true that that will require a degree of rote learning.
Regarding your second question, you must know the nominative, genitive and the gender for every noun. It just won't suffice to remember that “time” is tempus; you wouldn't know how to use it, and you wouldn't recognize it when reading O tempora, o mores. See this question (and the answers) for why this is so.
I'm not sure it's much of a tip, but I would say that it's easiest to just memorize these forms in the order that you see in most dictionaries, i.e., tempus, temporis, n. time; palus, paludis, f. swamp; malum, mali, n. apple; and so on. And please say these out loud or in your head to learn the vowel lengths, they're an integral part of the word.
Also note that the same applies to verbs, where you will usually recite first person singular present active indicative, then the same for the perfect, and then the perfect participle or supine.
