Rosh haShanah or Yom T'ru'a

Questions:

Which is the actual date for Yom Teruah?

Is Tomorrow the day to blow Shofar?

Also Rosh Hashanah is not based on the Bible right?

I thought the 1st month of the year was in Spring.

People explain this is agricultural start plus maybe Messiah will come back and start a new era but I thought Rosh Hashanah is the Rabbai's invented calendar .

The name Rosh haShana does not occur in the Hebrew bible, but the timing for this celebration is specified in Lev 23:24-25 (Num 29:1-6), where it is called Yom T’ru’a (יום תרוע):

Speak to the sons of Israel saying, “In the seventh month on the first of the month, you shall have a rest, a reminder by תרוע, a holy convocation.  You shall not do any laborious work, but you shall present an offering by fire to YHWH.

The reference to the seventh month refers to the amount of time that has passed since Passover.  (According to Ex 12:2 and 13:3, 4, Passover was to be observed on the first day of Aviv, spring, and this was to be considered the beginning of months for Israel.)  No name for the month of יום תרוע is stated in this context, but as traditionally observed this is a two-day celebration that begins on the first of Tishrei.  Tishrei is a Babylonian or Akkadian name for the seventh month; in point of fact none of the Hebrew names used today are preserved in the Hebrew bible or have their origin from classical Hebrew roots.  It is entirely possible that the months were originally tracked from Aviv merely by number as are the days of the week, except for Shabbat, to this day. Additionally, Aviv still means spring, but it no longer used as a name for any month. 

The source of your confusion is understandable, and it is shared by many people.  After all, the text in Exodus specifically states that Aviv is to be the beginning of months for the people of Israel.  From our existing perspective, this statement should mean that Passover starts on new year’s day.  The standard explanation for this is that at some time or other the Jews developed both an ecclesiastical year and a civil year; so Passover was the start of the ecclesiastical year, and Rosh haShana is the start of the civil or agricultural year.  This is how you will find the months tabulated in reference material.

Month Number*		Hebrew month	Length	Gregorian
Ecclesiastical/ Biblical	Civil
1	7	Nisan	30	Mar-Apr
2	8	Iyar	29	Apr-May
3	9	Sivan	30	May-Jun
4	10	Tammuz	29	Jun-Jul
5	11	Av	30	Jul-Aug
6	12	Elul	29	Aug-Sep
7	1	Tishrei	30	Sep-Oct
8	2	Cheshvan (or Marcheshvan)	29/30	Oct-Nov
9	3	Kislev	30/29	Nov-Dec
10	4	Tevet	29	Dec-Jan
11	5	Shevat	30	Jan-Feb
12	6	Adar	29	Feb-Mar
Total			353, 354 or 355

Now, I do not know when the name of the present celebration was changed from יום תרוע to ראוש השנה, but there is another alternative in understanding the passage in Exodus 13.  Throughout the Hebrew bible, the day that YHWH brought the descendants of Israel up from Egypt was the event that defined them as a special people apart, reserved for YHWH.  On the basis of this understanding, the first of Aviv was the beginning of months and years for Israel as a people, like a birthday.  As such it does not really have anything to do with an ecclesiastical year or a civil year.  These designations all came much later.

While the people lived in Egypt, they became familiar with the agricultural cycle as it existed there.  That is the Nile flooded in mid to late summer.  The people of Egypt had no idea why the cycle of the Nile was so completely out of sync with all other countries in the region, but without the Nile inundation, agriculture in Egypt would have been impossible.  Farming in the land of Israel required completely different timing.  Since there was no great central river, the Israelite farmers were dependent on the rains, Which started around the month of Tishrei and could last until the month of Adar.  Thus planting for the following year had to start in Tishrei, and harvest for annual crops occurred from early to late spring.  Only the most hardy crops of grapes and fruit trees could survive the summer.  This may account for the development of Yom Tru'a becoming the start of the agricultural year.