Shalom NewStart

I am reproducing the link from the main page which takes you to an article that I hope answers these questions.

As a quick summary: the death of Christ frees us from the PENALTY of the law, not the Law itself - thus rather than (for example) abolishing the commandment not to commit adultery (it would be lunacy to abolish it if you think about it) He removes the death penalty through His atonement on the cross if we repent genuinely. The story of the woman caught in adultery illustrates the place of the Law in the new Covenant - there is forgiveness so long as we do not cheapen grace by doing it again and again (my impression with the adultery was that she was given one more chance). Some parts of the Law have been fulfilled and are no longer binding - the animal and other sacrifices and the Levitical priesthood system that administered it. We're now under a New Covenant and a new (Melchizedek) Priesthood. But not eating pork (fore example) is still in force - it's bad for our health because according to Yahweh it isn't food (even if people may call it food).

Now to the more important question as to what being "under the Law" meant - I refer you to this article and specifically to this section:

Works of the Law and Under the Law
Much of the confusion about Paul's teachings on the Torah involves two scripture
phrases which appear in the New Testament only in Paul's writings (in Rom. Gal. &
1Cor.). These two phrases are "works of the Law" and "under the Law", each of which
appears 10 times in the Scriptures.

The first of these phrases, "works of the Law", is best understood through its usage in
Gal. 2:16. Here Paul writes:
knowing that a man is not justified by
WORKS OF THE LAW but by faith in
Yeshua the Messiah, even we have believed
in Messiah Yeshua, that we might be justified
by faith in Messiah and not by the
WORKS OF THE LAW; for by the WORKS OF
THE LAW no flesh shall be justified.
Paul uses this phrase to describe a false method of justification which is diametrically
opposed to "faith in the Messiah". To Paul "works of the Law" is not an obsolete Old
Testament system, but a heresy that has never been true.
The term "works of the Law" has shown up as a technical theological term used in a
document in the Dead Sea Scrolls called MMT which says:
Now we have written to you some of the
WORKS OF THE LAW, those which we
determined would be beneficial for you...
And it will be reckoned to you as righteousness,
in that you have done what is right and good
before Him...
(4QMMT (4Q394-399) Section C lines 26b-31)
The second of these phrases is "under the Law". This phrase may best be understood
from its usage in Rom. 6:14, "For sin shall not have dominion over you, for you are not
UNDER THE LAW but under grace." Paul, therefore, sees "under grace" and "under the
Law" as diametrically opposed, one cannot be both. The truth is that since we have
always been under grace (see Gen. 6:8; Ex. 33:12, 17; Judges 6:17f; Jer. 31:2) we have
never been "under the Torah". This is because the Torah was created for man, man was
not created for the Torah (see Mk. 2:27). "Under the Torah" then, is not an obsolete Old
Testament system, but a false teaching which was never true.
There can be no doubt that Paul sees "works of the Law" and "under the Law" as
categorically bad, yet Paul calls the Torah itself "holy, just and good" (Rom. 7:12),
certainly Paul does not use these phrases to refer to the Torah itself.
In order to preserve the intent that these two phrases were technical theological
terms I have rendered the Aramaic phrase for “works of the Law” with the Hebrew
phrase “Ma’aseh HaTorah” (“Works of the Law”) which is the exact Hebrew phrase
found in the Dead Sea Scrolls (MMT). In the same way the technical term for “under the
Law” has been transliterated from the Aramaic as “T’cheit Namosa”.
lix

Torah and Nomos
The Hebrew word which the KJV renders “Law” is “Torah” which actually means
“guidance; instruction). The Greek word used in the Greek NT is NOMOS. While this is
generally taken as a Greek word it is also an Aramaic word. There are two Aramaic
words for Torah. The actual Aramaic cognate of Torah is )tyrw) “Orita”. Orita is the
word which appears for Torah in the Targums and Talmuds. The Peshitta Aramaic
Tanak however uses the Aramaic word )swmn NAMOSA for Torah. NAMOSA is based
on a three letter Semitic root smn meaning “to civilize”. The same root is used in
Modern Hebrew to mean to be polite. The Aramaic NT also uses the word )swmn for
“Torah” (except in Mt. 11:13; 12:5; 22:40 where )tyrw) is used. I have always
translated )tyrw) as Torah. Wherever )swmn seems to refer to the Torah I have
translated “Torah” as well.

I hope this helps.