You can get a more detailed and more expertly concise history on this from /r/AcademicBiblical

A short answer here is that practitioners of biblical textual criticism, who study the history of manuscript transmission with a view to creating a critical editions of biblical books that are as close as possible to the originals, are fairly certain that the original language critical editions they produce are not exactly identical to the original autographs (original copy) of the biblical books. Even if one book was identical, it is impossible to know for sure.

Considering how many centuries the process of of copying and translating manuscripts endured, the modern critical editions of the biblical texts are accurate enough to be useful. An interesting example of accuracy in the history of manuscript transmission is the discovery of the dead sea scrolls. The Isaiah scroll is 1000 years earlier than the earliest known manuscripts prior to its discovery. Although there are variant readings and alternative spellings, the text is in surprisingly close agreement with manuscripts that were created a 1000 years later.

The extent of differences generated in the history of transmitting biblical texts varies from book to book. An interesting study on text critical issues for the New Testament relative to the issue of the theological biases of the early church introducing variant readings in the text is "The Orthodox Corruption of Scripture" (Ehrman).

Text Critics do not "know" which of the variant readings on a particular verse is correct. They make guesses. There are criteria for determining which variant reading will be preferred. In the new testament, for example, those criteria are grouped into two categories: External Criteria and Internal Criteria.

External evidence focuses on the date and quality of the manuscript witnesses. The geographical distribution of the witnesses and the genealogical relationship of the witnesses to defined families of manuscripts are considered. Internal evidence focuses on criteria such as: the more difficult reading being preferred, where "difficult" is a difficulty in copying for the scribe as scribal emendations tended to clean up the text. The shorter reading tends to be preferred. Variants that are verbally dissident tend to be preferred as scribes tended to harmonize. (for a full run down on the criteria see Metzger's "Textual Commentary on the Greek New Testament")

The final decisions pertaining to which variant is right (that is to say which variant will wind up in the critical Hebrew/Greek edition that becomes a basis for English or other language translations of biblical books) is not done under the guise of "knowing" which is correct. It is all educated guesswork but done in a process that has some measure of integrity and success.

/u/filosophikal has given you something of an answer that focuses on the reliability of the texts in question, but it seems to me that you are more interested in the question of translations?

So I know that parts of the Bible are pulled from many different texts written in multiple different languages over centuries.

The Bible is written in three languages. Primarily Hebrew (most of the Old Testament), Aramaic (a couple of small sections of the Old Testament), and Koine Greek (the New Testament). It comprises multiple texts, but those texts are not 'pulled' from other texts. That is, the Bible is more like a small library of books, not one 'composite' book.

Can we say for certain that we know all the texts have been translated correctly?

I work primarily on Greek language things, we have a continuous history of knowledge of Greek and scholarship in Greek, i.e. there has never been a period where people haven't taught and learnt Greek. While translation is an art, the general understanding of the text of the New Testament is not in doubt. There have been mistranslations throughout history, or less-than-perfect translations, into various languages, but our understanding of the Bible is not based on those translations, it's based on reading the books in the original languages.

As for Hebrew, there has also been a history of Hebrew scholarship, though it is true that there are things in the Biblical text that are stubbornly obscure. For example, animal and plant names are often difficult to be exact about. Nonetheless, our general knowledge of Hebrew, and Aramaic, is quite sound.

Or has it been altered either on purpose to make people believe a certain thing, or on accident due to lack of linguistics in the past and mistranslation?

If you are talking about altering the texts in the original languages, this relates to the textual criticism discussed in other answer. In short, any systematic alteration of the texts of any reasonable size occured at a stage prior to the texts we have. Which means it would be mostly speculation to say, "well, this was altered before any existing copy" - how would one know that?

I mean the Bible has to have been translated a lot in the past from Roman, Hebrew, Greek, ect. I just find myself doubting its been translated correctly wholly sometimes.

It sounds like you might have a common misunderstanding that the Bible as used and thought of today, in English, is the result of a process of serial translation, e.. from language X to Y to Z to A to B to English. That's not accurate at all. Modern English Bibles, for the most part, represent translations of carefully evaluated critical editions of original language texts, with a considerable wealth of linguistic knowledge.