h, OK, let's take a closer look at this:
This is the law: Art. 237 INA:
(2) Criminal offenses
(A) General crimes.-
(i) Crimes of moral turpitude.-Any alien who-
(I) is convicted of a crime involving moral turpitude committed within five years (or 10 years in the case of an alien provided lawful permanent resident status under section 245(j)) after the date of admission, and
(II) is convicted of a crime for which a sentence of one year or longer may be imposed.
This is the first removal ground under the criminal section:
Any ONE crime of MORAL TURPITUDE within a CERTAIN TIME AFTER ADMISSION and for which ONE YEAR or more is a possible sentence.
Since misdemeanors usually are defined as crimes with a maximum sentence of 1 year in most cases only felonies would qualify here. They have to be a crime of MORAL TURPITUDE, which is defined under immigration law, regardless what the state calls them.
Always remember, that the inadmissibility provision concerning crimes of moral turpitude is very different. This here is the removal, or deportability, provision.
Now on to the next:
(ii) Multiple criminal convictions.-Any alien who at any time after admission is convicted of two or more crimes involving moral turpitude, not arising out of a single scheme of criminal misconduct, regardless of whether confined therefor and regardless of whether the convictions were in a single trial, is deportable.
Now this is different. If you are convicted of TWO or more crimes of MORAL TURPITUDE there is NO TIME limit anymore and NO LIMIT as to the maximum sentence.
Therefore you can be deported after being convicted for 2 misdemeanors of moral turpitude committed any time and even if only sentenced to a fine.
(iii) Aggravated felony.-Any alien who is convicted of an aggravated felony at any time after admission is deportable.
That is pretty clear. If in dispute, federal immigration law will control what felony is aggravated or not, but usually the courts go along with the state definitions.
Some other crimes that make one removable are these:
(iv) High Speed Flight.-Any alien who is convicted of a violation of section 758 of title 18, United States Code, (relating to high speed flight from an immigration checkpoint) is deportable.
Very important is that drug and gun law violations are being treated separately:
(B) Controlled substances.-
(i) Conviction.-Any alien who at any time after admission has been convicted of a violation of (or a conspiracy or attempt to violate) any law or regulation of a State, the United States, or a foreign country relating to a controlled substance (as defined in section 102 of the Controlled Substances Act (21 U.S.C. 802)), other than a single offense involving possession for one's own use of 30 grams or less of marijuana, is deportable.
(ii) Drug abusers and addicts.-Any alien who is, or at any time after admission has been, a drug abuser or addict is deportable.
(C) Certain firearm offenses.-Any alien who at any time after admission is convicted under any law of purchasing, selling, offering for sale, exchanging, using, owning, possessing, or carrying, or of attempting or conspiring to purchase, sell, offer for sale, exchange, use, own, possess, or carry, any weapon, part, or accessory which is a firearm or destructive device (as defined in section 921(a) of title 18, United States Code) in violation of any law is deportable.
This language is pretty clear, too.
(D) Miscellaneous crimes.-Any alien who at any time has been convicted (the judgment on such conviction becoming final) of, or has been so convicted of a conspiracy or attempt to violate-
(i) any offense under chapter 37 (relating to espionage), chapter 105 (relating to sabotage), or chapter 115 (relating to treason and sedition) of title 18, United States Code, for which a term of imprisonment of five or more years may be imposed;
(ii) any offense under section 871 or 960 of title 18, United States Code;
(iii) a violation of any provision of the Military Selective Service Act (50 U.S.C. App. 451 et seq.) or the Trading With the Enemy Act (50 U.S.C. App. 1 et seq.); or
(iv) a violation of section 215 or 278 of this Act, is deportable.
Very important is also to watch the domestic violence provision:
(E) 6/ Crimes of Domestic violence, stalking, or violation of protection order, crimes against children
(i) Domestic violence, stalking, and child abuse.-Any alien who at any time after entry is convicted of a crime of domestic violence, a crime of stalking, or a crime of child abuse, child neglect, or child abandonment is deportable. For purposes of this clause, the term "crime of domestic violence" means any crime of violence (as defined in section 16 of title 18, United States Code) against a person committed by a current or former spouse of the person, by an individual with whom the person shares a child in common, by an individual who is cohabiting with or has cohabited with the person as a spouse, by an individual similarly situated to a spouse of the person under the domestic or family violence laws of the jurisdiction where the offense occurs, or by any other individual against a person who is protected from that individual's acts under the domestic or family violence laws of the United States or any State, Indian tribal government, or unit of local government.
(ii) Violators of protection orders.-Any alien who at any time after entry is enjoined under a protection order issued by a court and whom the court determines has engaged in conduct that violates the portion of a protection order that involves protection against credible threats of violence, repeated harassment, or bodily injury to the person or persons for whom the protection order was issued is deportable. For purposes of this clause, the term "protection order" means any injunction issued for the purpose of preventing violent or threatening acts of domestic violence, including temporary or final orders issued by civil or criminal courts (other than support or child custody orders or provisions) whether obtained by filing an independent action or as a pendente lite order in another proceeding.
Now to your questions:
1) If the aggravated assault is classified as a misdemeanor under state law, it will not have a maximum sentence over a year, therefore it will not be an aggravated felony under (iii) and not a crime under (i), so if it is the only conviction, it would not make a person removable, except if it is in connection with domestic violence under (E)
But if there is another conviction then the offender will be removable under (ii)
2) Crimes of moral turpitude are defined as such under federal immigration law. The courts will look there, not at state law, to decide. For removing (deportation) purposes the actual sentence received is irrelevant! Under (i) only the possible maximum sentence is relevant. What you are probably remembering are the inadmissibility provisions which are very different from the deportation provisions.
Moral turpitude has nothing to do with the usual classifications of crimes as misdemeanors, felonies or similar like "petty offenses" etc. MT is an additional qualification that can be added to any class of crime.
3) About the expired green card, the border inspectors will not let you enter the country if your green card is expired.