Proper grammar/punctation with "e.g." and "i.e." usage and "however"....

Hello, my confusion is with how to structure a sentence correctly with "i.e." and "e.g.". I have seen "i.e." spelled out as follows:

"My dog and cat went fishing, i.e., they took the rods and caught some big fish."

However, that seems off to me a bit, possibly because I'm used to omitting the comma, despite writing "however" as follows:

"I wished to jump off the ledge, however, now I'm happier and hopeful."

But I see people writing from variations as follows:

"I want to visit Sherlock, however he is not home."

"June is the month of May, however May is not the month of doom."

I realized however may not need a comma if written out like this:

"I began to swim, and I had swam, but, however I swim, I always have swam."

The problem I have are the conditions and hard rules, such as if it's wrong to simply remove both commas, or if one only is always correct:

"I want to walk, I want to jump, he says, but he can't (e.g., he has no limbs)."

OR

"Trust the feathered man, for he has forsaken us all, i.e. we are limitless in nature."

So my questions are, is omitting both commas fine, or, when necessary, do both NEED to be there? And what are the rules with regards to parentheses usage? Thanks for your help.