From this Hebrew article from the Haaretz newspaper dated September 5, 2008, titled "The Bible in translation to Modern Hebrew", with subtitle "87 year-old teacher publishes 14 pamphlets with a translation of the Bible [OT] to modern Hebrew raises controversy in the education system", you can see that Biblical Hebrew is not easy for Israeli kids to read. However, the fact that the article is from 2008 shows that until now no one thought that the difficulty was so great that our kids needed a translation. In any event, the article is talking about the secular schools. In the religious school system there is no question, the Masoretic text is used and kids do fine with it.
The IDF still gives out Masoretic text OT's to each new inductee, and commanders still quote from it, as do politicians.
I would say that the metric between modern and OT Hebrew, in its various dialects, is like modern English to Shakespeare's English, not modern English to Chaucer's English. The metric of Hebrew to Aramaic is like French to Italian.
There are several languages that we call Aramaic - Daniel, Jonathan, Onkelos, Talmudic, Syriac and modern. The Aramaic of Daniel and the Jonathan targum is apparently the vernacular of the first century and earlier. The Aramaic of the Onkelos targum and the Talmud are a similar, maybe later dialect. I can read Onkelos and even speak a little Talmudic Aramaic, as can most Israeli men trained in the religious education system. We sometimes use a silly pidgin of this language to speak privately in the presence of children, wives or secular Israelis. I have difficulty with Daniel and with targum Jonathan and need a dictionary. In the Old City of Jerusalem there is an Armenian community that speaks a modern Aramaic. We do not understand it either in writing or spoken. The Syriac Peshita is another form of Aramaic that we can read with the help of a dictionary though it is more challenging than targum Jonathan.
Apart from the problems of vocabulary and grammar, there is a stylistic problem and a cultural problem. Some of the OT (e.g. Job, Psalms) is written in a literary style that would make it a difficult read even if it were in modern Hebrew. Other parts such as Songs and proverbs have cultural references that are foreign to the modern mind.
The Mishnah is "easy Hebrew" for the speaker of modern Hebrew, apart from the subject matter, which requires a commentary to follow. The style of the Mishnah is simple, mnemonic prose, not at all "literary". It does have an ample sprinkling of Greek and Latin terms that require footnotes.