This may be somewhat confusing, but here it is: Printed Jewish calendars, or books that outline the order of prayers through the year, will begin with the month of 'Tishrei' ... the month in which Rosh Hashana, "Head of the Year", occurs ... usually corresponding to sometime in September. The next month ... second in the printed calendar ... is 'Cheshvan'. But the Torah refers to those months as the seventh and eighth months respectively. As far as the Torah is concerned, the first month is the month of 'Nissan' ... the month in which Passover occurs ... corresponding to some time in March or April. On that basis, the second month is 'Iyar'.
Adar.
Depending on which Hebrew year you are looking at (civil or ecclesiastical), it is either Elul (אלול) or Adar (אדר)
Technically speaking, the 12th month is Adar (אדר).However, the common ordering is to place the 7th month first because the year changes in the 7th month. So in this case, Elul (אלול) is the 12th month.
Actually, it is a Hebrew girl's name derived from the Hebrew month of Sivan (סיון) which is in late Spring.
The name June has no meaning in Hebrew. Your only option is to write it phonetically as גיון The Hebrew word for the month of June is yooni (יוני) but this word is not used as a name in Israel.
Iyyar is the name of a Hebrew month, that falls in the Summer.
Cheshvan
No. This word is a made up word that some Christians use for the name of God. It resulted from a 12th Century mispronunciation of the actual Hebrew name of God.See The Tetragrammaton for more information about the name of God.
The 12th month is spelled "December."
Shevat. It doesn't correspond to February exactly, but it is the Hebrew month that (on average) has the greatest overlap with February.See also:How the Hebrew calendar works
There are 12 months in the Hebrew calendar. In a leap year there are Adar A and Adar B. Adar is the sixth month.
Elul (????) is the 6th month on the Hebrew calendar. The name of the month, like all the other Hebrew months, was brought from the Babylonian Exile. Elul originated from the Akkadian word for "Harvest". A similar month name was also used in Akkadian, in the form el?lu.