That's it, for example, is it acceptable to say Люблю тебя, or do you have to use я Люблю тебя. Or читал книгу instead of Я читал книгу?
Actually you are asking about whether Russian is a pro-drop language. A pro-drop language, according to Wikipedia, is a language in which pronouns are usually omitted when they can be inferred.
For example, Spanish and Portuguese are classical examples of pro-drop languages. "Te quiero" (I love you) can be heard way more often than "yo te quiero" just because verbs are conjugates in Spanish, so that you in a moment recognize contextual pronoun.
Now let's go back to Russian. The simplest valid answer we can give - Russian is partially pro-drop. The actual degree of this "pro-dropness" is an open issue and a subject to debates. Here's another relevant quote:
There is disagreement as to whether Russian has pro-drop (alternatively, subject pronoun omission is treated as an instance of contextually licensed ellipsis).
For further information I'd recommend you to checkout the last link, but to sum it up: Russian is a pro-drop language, but less pro-drop that Japanese or Spanish. There are some reasons for this, one of most notable is lack of information we can get from verbs in past tence. [Он] читал / [я] читал / [ты] читал will be indistinguishable without context.
No. If you want just say "I love you", you should use the pronoun "Я люблю тебя". Omitting the pronoun here is marked.
"Люблю тебя" sounds as if the phrase was unfinished. It is ok to omit pronouns if
- It is an answer to a question.
-Ты кого любишь?
-Что ты делаешь?
- Or if the sentence will be continued:
-Люблю тебя за твою улыбку.
-Люблю тебя, красавица.
Note that the last sentence has an overtone of being a joke or just telling something already well known to her, it is not suitable if you want to make a confession or just to say you love her for the first time.
Russian is partly pro-drop. Not nearly as much as other Slavic languages or Romance languages.
This actually varies among Slavic languages. In some like Czech and Polish it is very acceptable and in fact, unmarked to omit subject (and sometimes object pronouns).
E.g. (QW=question word)
Polish Q: Czy kupi-ł-eś banan-y?
QW (perf)buy-past-2sg.MASC banana-PL
"Did you buy bananas?"
A: Tak, Kupi-ł-em
"Yes I bought them (lit "yes bought")"
If you had the pronouns in this sentence, especially for the question, it would sound weird, like you were emphasizing "YOU" (did YOU buy bananas?). In Russian however... "ты купил бананы?" does not sound marked, and it is better to have the pronouns.
This same conversations couldn't happen as easily in Russian. In Russian pro-drop usually only occurs in the present and future tenses. In the past it is very confusing.
*дал им книги
da-l im knig-i
give-masc 3ppl-DAT book-PL
"I/he gave them books" This sounds pretty bad and is highly ambiguous. I am sure it could happen, but would be marked, unlike in Polish, Czech, or Romance languages like Spanish.
What Brian Collins said is not correct. In colloquial Russian, it's perfectly fine to say "Купил бананы?" - "Купил." ([you] bought bananas? [I] bought.), omitting the pronouns altogether. There's no ambiguity here, it's easily inferrable from the context. However, in written language, you usually prefer not to omit pronouns, because it sounds "lazy", like you don't care.
Subject pronoun is not necessary, but it is implied by the verb's person (люблю тебя, любим тебя).
You don't have to have an object, too (Пока! Люблю! = Bye! Love you!).
Now, there are impersonal sentences where you use it or they in English but you don't use any subject in Russian (it's getting dark = темнеет, they say you learn it = говорят, [что ты] учишь).