Ok, so--the basic question here is whether or not Hebrew is fully understood. The answer is, "Well...yes and no."

SO, you're specifically asking about ancient Hebrew, which is in and of itself a very complex thing. Languages evolve over time and we have Hebrew texts from over a millennium--so we have many different PERIODS of Hebrew, some of which we know and understand better than others.

Resources: Gogel's Grammar of Epigraphic Hebrew; J. Naveh The Early History of the Alphabet; C. A. Rollston's 2006 BASOR article on scribal education; F. M. Cross' Leaves from an Epigrapher's Notebook; also pretty much every Classical Hebrew reference Grammar (Bauer/Leander, Waltke/O'Connor, J. Blau, etc. etc.).

As /u/suggestshistorybooks has, well, suggested, the earliest Hebrew inscriptions appear in the Phoenician script. To be fair, at that point, we can't tell whether the inscriptions are Phoenician or whether they're Hebrew (there simply aren't any linguistic isoglosses present in those inscriptions [e.g., the Gezer Calendar] to distinguish between the two languages).

By and large, we have the script development stuff figured out. There are still lingering questions about the Iron Age IIB (c. 10th century BCE-ish). We simply have very little epigraphic data from this time period.

The further we progress through the 1st mil. BCE, the more linguistic data we have. Once we get to the 8th century, we start to see a lot more texts and inscriptions.

Ok--so, as far as BIBLICAL Hebrew is concerned, we know a lot and can get a decent grasp on translating just about everything. There are a lot of words we don't really understand, though. Sometimes the syntax is really freaking weird. The whole enterprise is tricky because the language is dead, so it's not like we can just go up to a native speaker and say, "Hey, could you help me out with this?"

There's still a lot of debate about the nature of the verbal system (is it tense based or is it aspect based?). Rob Holmstedt is very involved in this conversation. A big part of the debate has to do with literary genre and the MODE a scribe decided to utilize when composing a text.

There's also the whole ORALITY aspect of the issue, which is very much in vogue now in the secondary literature (see D. Carr's Writing on the Tablet of the Heart).

Suffice it to say for now, we generally have a decent idea about the language writ large; however, there is a great deal we have yet to fully discern...there are large gaps in our data set, but we've been able to triangulate a lot of things that were later confirmed by discoveries of other Northwest Semitic Languages (like Ugaritic's decipherment in 1929).

This question confuses me a little bit. First, do you mean a Hebrew script or language? Second, do you mean the Semitic language group or Hebrew, specifically?

The oldest texts of the Hebrew language exist in Phoenician script. The Old Hebrew script (oftentimes called Biblical Hebrew), specifically, developed out of the Phoenician script c.1000 BCE, and its development is fairly straightforward, and well understood. Now, the broader Semitic language group extends further back, but incorporates a lot of different scripts and languages, and its origins are less understood.

This question may be more appropriate for /r/linguistics, but it needs to be more precise, first.