I understand that MONTHS abbreviations is done by using the [three first letters + period] of each month. Is it true?
Jan.
Feb.
Mar. or March??? (not abbreviated)
Apr. or April??? (not abbreviated)
May. or May??? (not abbreviated)
Jun. or June??? (not abbreviated)
Jul. or July??? (not abbreviated)
Aug.
Sep.
Oct.
Nov.
Dec.

Or there is a rule regarding not abbreviating "short" months like March, April, May, June & July.

Regards

The months that you may see abbreviated are:
Jan.
Feb.

Aug.
Sep.
Oct.
Nov.
Dec.

If you want, then:
Mar.
Apr.
Jun.
Jul.

No abbreviation :
May