Learn English – Can we use the abbreviation “etc” without a period/full stop

There is a specialist, conventional use of the colon in the Bible (not just KJV) in rendering the psalms into English. Here the colon separates the two halves of the Hebrew verse:

The Lord is my shepherd; I shall not want.
He maketh me to lie down in green pastures : he leadeth me beside the still waters.
He restoreth my soul : he leadeth me in the paths of righteousness for his name's sake.
Yea, though I walk through the valley of the shadow of death, I will fear no evil : for thou art with me; thy rod and thy staff they comfort me.
Thou preparest a table before me in the presence of mine enemies : thou anointest my head with oil; my cup runneth over.
Surely goodness and mercy shall follow me all the days of my life : and I will dwell in the house of the Lord for ever.

Normally it's written with a space on both sides, to make clear that it's a division rather than a normal colon.

british-english

As indicated in the comments, it's not a question of grammar (even though it is a question about punctuation), it's a question of style.

In your example, Jack Russell is represented by a symbol: J.R. or JR (either with or without a space), or even a picture of a terrier. In that case, it really doesn't matter what the symbol is.

There is more of a question about whether full-stops should be used in names or for other abbreviations:

• Mr. J. R. Ewing
• Mr J R Ewing
• John R. Ewing III
• John R Ewing III
• viz.,
• i.e.

Current British practice is to omit many of these full stops. It's fussy and they aren't really necessary to show that the word is an abbreviation: it's unlikely that Mr Ewing's middle initial is just "R". I generally use my middle initial, and never use a full stop. Even a less obvious abbreviation like viz is (it appears, subjectively) losing its customary full-stop.

I suspect the reason for this is that additional stops

• need interpreting to see if they are the end of a sentence
• take an additional keystroke, or time to write

and both of those are reasons in this hectic age to omit dots.

But this is still a matter of style: to use a full-stop may be prescriptively required, but it does nothing to enhance the descriptive function of an initial or other abbreviation.